"99 Percent" Miss This. What Is The Length?
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- เผยแพร่เมื่อ 7 ส.ค. 2019
- It may not be exactly 99 percent, but many people will get the incorrect answer. It's a great teaching opportunity. Learn how to solve this problem! (There are multiple ways, I am presenting one valid method).
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Great! Thanks for the shout out. My only thought at the end was that people might be left thinking "so why did it give the right answer before?" It might be nice to point out the coincidence of the original height of 4.
Thanks for the feedback! I will think about this, but I haven't come up with a good explanation really! In the original problem, I did notice the answer was 8 = 5 + 3, so I did try to do the "shortcut" way of drawing 3-4-5 triangles. But I didn't have a convincing proof of why the horizontal lines were coincident and also parallel to the top line, so I figured it was a coincidence. I then suspected someone would find a valid proof. So I was surprised when so many people merely used the incorrect method without proper justification! I suspect someone will email me a good reason.
@@MindYourDecisions You can see why it must work if we build up the shape differently. Start with a 4x5 rectangle and build a 3-4-5 triangle on the right side and another to the bottom edge to match this shape. Then remove the bottom and right edges of the rectangle. We've now recreated this shape, save for proving that the angle on the bottom right is 90°. But that's a simple proof. That angle is the sum of two angles we created. the right side is the 4-5 angle from a 3-4-5 right triangle. The left side was the complement of the 4-5 angle of a 3-4-5 right triangle.
We now have enough information to conclude that the original shape and our constructed shape must be identical. If we try this again with the 3x5 rectangle as our starting point, we end up failing to prove that the bottom right corner is a right angle, since it would be the sum of a 3-4-5 right triangle's 4-5 angle and the complement it's 3-5 angle. Which cannot be 90°.
@@MindYourDecisions I don't think there's a good proof for it other than that you can attach a 345 triangle to the right of the 5 line by extending the 4 line of the smaller 345 triangle by 3, so that you always get a 4 line on the right side, now if you say that the left line is 4 it just aligns which it will not do for any other number
Not true. The two "3" sides on the left side of the problem with the 90 degree angle mean that the remaining side of the short triangle is zero, hence, the correct answer to the problem is the square root of 41.
@@MindYourDecisions Well, I have found the condition for the lengths. Assume we want to find the height (in the first video 4, here 3) so that the "wrong" solution is right. Then the height = (the length of 4 from video)*(the length of 5 from video)/(square root of (the legth of 3)^2 + (the length of 4)^2). You can put any numbers instead of 3, 4 and 5 and find the height. It is all based on similarity of triangles. I can try to write more proper solution once I am back home.
Lets assume you have height of 3 and legths of 3,4 and want to find something instead of 5. According to my solution the missing length is sqrt(3^2+4^2)*3/4 = 3,75. So in this video, if the last length is 3,75 instead of 5, the incorrect method will lead to the same solution.
In fact, I have found the condition that the incorrect method produces the same result as the correct method ;-)
Always take that "Diagram not to scale" warning seriously
Gotta learn that the hard way
But scale isn't the same as proportions.
I always thought it just meant you can’t use a ruler 🤦♂️
@@kubush Yeah original plot is very misleading.
If it's not scale, it's false, he changes the problem after asking the question? And I thought these were honest questions?
The error is 99% of people who tried this, assumed that you drew it correctly in the first place.
@@Mausoc I don't think you understood the error, then... The problem is not the answer but the used method.
The "99% error" is assuming that a line equals 4 when there's no reason to, as you find the same answer no matter the actual length of the lines
Ah, therein lies the lesson. It's okay to assume, but verify your assumptions are correct.
He changed a number in the problem and got a “wrong” answer lol I wasted my time watching this
I just saw that not to scale was acceptable, so my answer was also not to scale.
@@willhanlon5863 Did you even watch the video? People were using a method that just happened to turn out correct in that specific case. As shown that when you change the length of any line, the method doesn't work anymore. It's like when a kid sees x^2 for the first time and the first example says, 2^2 = 2 and then assumes that 3^2 = 6. Theres no proof given at any stage that moving said line would connect to the 2nd right angle, it's an assumption people made and the answer just happened to fit.
didn't think about rearranging the lines like that! You solved this so much more elegantly than I. I wrote out a system of equations then spent half an hour solving them 😆
I think that's where the illustrated approach really helps, a lot of people (including myself) think of the algebraic approach first, without thinking about possibility of rearrangements.
you still solved it !
Good problem. I eventually got this right, but I only got a decimal approximation because I used the sine function a lot. Always nice to have many ways to get to the solution.
Ah yes, the "not to scale" diagram. Another one of those things teachers like to laugh about in the break room after everybody failed the test.
It’s kind of a dirty trick tbh
@@bobbytrap2554 not really, it tells you that it's not to scale and it's expected that you actually "solve" the problem instead of just using a ruler.
Yes, but this test gives a good insight into maths. It's like hooping a basketball, we're never as accurate as we believe we are.
@bobbytrap surely not using a ruler is why you fail this question. if you were to measure it on the page you would see that the lengths were totally off and that would definitely prompt you to work out the answer using the numbers.
@@ryansmith9138 Yeah. My problem was I have no grid paper, ruler within reach and I wasn't going to wait ten minutes to open up an art program and try to make a grid in it and then draw in it just because someone else can't be bothered for their own TH-cam video and just recycled the diagram from a different problem.
I did find these though:
www.ginifab.com/feeds/angle_measurement/
www.mathsisfun.com/algebra/trig-solving-triangles.html
As many have said the question itself is somewhat misleading, but because I work as a 3d draftsperson I can promise those questioning the drawing that sketches from customers (boss's) can be much worse. If you work with only known information instead of implied information you are much more likely to give the customer what they want.
It is very interesting for a person from a completely different country to develop the exact same process as me. Even without translating, the video was understood. Math hooray!
Yeah same
how are u typing english then
@@doraelog690 I used a translator after writing down Korean.
@@TheHorrorsPersistButSoDoI I don't quite understand what you're saying. What is Collatz concepture?
@@TheHorrorsPersistButSoDoI Oh, I see. Thank you for your kind explanation of the Collatz conjecture. I hope someone who can answer your question will come!
Thanks for drawing it in such a purposely misleading way.
*Really helpful*
THE DIAGRAM IS ALWAYS WRONG.
EVEN WHEN IT'S RIGHT, IT'S WRONG.
Academy, Khan
Yap
This
Stop shouting your post in all caps.
I think a useful way of looking at this problem is by transforming it into a simpler problem that most people would recognize. In this case you can make the shape convex by flipping over the first right angle lines thus creating a quadrilateral. From there most people would realize the method for calculating the side.
I spent like 3 hours trying to solve this because my teacher wanted me to have a try (this was 2 months ago, and i did get it right) … then this month i found you channel
Highly recommended. Easy to understand. Thank you so much for saving my time.
Oh, that's easy. It's 12 1/4" - I measured it on the screen.
Whit what
@@ashirbadbehera4129 Whit a whruler.
My screen is smaller than that, so?
@@jlnbroadcast aouko
Your ruler must be wrong. My ruler measures it ~6 1/2.
This man is taking high school maths to the next level. Thanks for challenging the idle mind!
FOLLOW-UP COMMENT: (BTW, I DO LOVE YOUR VIDEOS.) I wanted to see why we got two different answers - I obtained 8 (in two different ways); you obtained sqrt(71). While your *method* is correct, your answer of sqrt(71) is for the *revised* problem where the left most vertical line segment is of length 3. With the *original* problem, that segment had length 4 --> so using your logic, your answer for the *original* problem would be x^2 = (sqrt(80))^2 - 4^2 = 64 --> x = 8, which was my answer (along with a few others.) Perhaps you could add a comment at the end of your video, since the length of interest was labelled x in both cases.
Thanks for leaving “drawing not to scale” out of the thumbnail
Even if that note was there I would have noticed the different lengths of the two "3" lines before I read the note.
@@stevenvanhulle7242 No you wouldn't have. 1:23 shows they were drawn exactly the same which was the point.
@@brandonfrancey5592 Except that, in the thumbnail, the leftmost side is given as 3, whereas at the start of this video, it's given as 4...
@@brandonfrancey5592 Uhm, yes. It was obvious really. When the angle is 90°, the opposing side cannot be the same length as one of the adjacent sides. You see that at a glance
@@stevenvanhulle7242 Even when I know not to trust anything that's not specified, I was still saying 'that is not a triangle' and 'that is not a parallel line' over and over again because I kept thinking they were.
"diagram not to scale" is a cheap way to make a problem way more difficult than it would be in a real life situation
Actually when we sketch things in the field, we don't do anything to scale, but solely rely on dimensions and shapes...we nice it
up when we get back to the office. That's the way it is in the real world of survey and engineering.
Is this a Steven Universe reference?
@@Wormhole798 yes, and presenting a problem for a student should be "niced up". you sketch when you already have the skills to unsketch it, not beforehand
@@beevee7078 i dont know what that is, so no
Yep, stuff like this is why I lost interest in mathematics, after taking part in competitions featuring problems just like this one. Instead of being in any way clever, far too many people rely on cheap shots like this that would get them laughed out of the room in a real world situation.
👏 brawo. Ja zrobiłem to źle nie pomyślałem nad rużnicom wysokości.
Dziękuję za pokazanie poprawnej odpowiedzi.
I love your channel and concepts you teach , really great !
The scale of the figure is the most deceiving part of geometry. Most people use wrong procedure because they seem the right way in the given scale.
Apparent scales are completely irrelevant - you should ALWAYS work with actual numbers, variables and geometric relationships.
If you said that something was twice as big as something else in a Geometry test just because it looked twice as big then you would get 0 marks on that problem.
@@Peter_1986 There are some problems with that. First it's just how the human mind works. We see something and immediatly make connections. Second is that even if the scale is wrong it's generally just smaller or larger, the relations between each number stays the same. And third, if the scale is wrong to this degree then why even bother with a diagram? May as well train people to draw out a figure from the numbers of the text. Personally I think the diagram should always give the right idea and what a person should do is to find a way to prove it mathematically.
@@shadowcloud1994
Yes, a diagram should preferably resemble its intended values.
For example, most people would get very emotional if they saw an image of an angle that claimed to be 90° but actually looked like a small acute angle.
Those diagrams are pretty annoying, and can cause some confusion.
Perfect example when drawing scales don't matter
@@Peter_1986 I agree there's no point of drawing a diagram if it isn't intuitively correct. Your example was spot on. The diagrams should clearly indicate that the side is not 3.
Whenever something is not drawn on scale, never assume a "horizontal" line is horizontal.
it kinda has to be since there are 90° marks
@@nathanyam2310 So, because there are three right angles you deduce that the lower two vertices are at the same height? That's so... odd.
@@stevenvanhulle7242 well no that isn't true.
@@stevenvanhulle7242 look at the angle between the side lengths that are 3 units long, that angle can be any angle since it is not defined. So then those two lower vertices can be at different heights but you can't really determine where they are located based on the graphic.
Horizontal is meaningless anyway, it's just to describe a line to talk about it. You could also give it a name like 'a'.
Yay! This is the first time I paused the video when Grant prompted and I got the answer right!
It's even simpler if you use the original value of 4 on the left hand vertical length.
Move the diagonal 4 to the other end of the diagonal 3 (as Presh did) and add the 3 to the 5 to get a side of 8.
You now have two congruent triangles (side of 4, right angle and a shared hypotenuse), so the top length is 8 too!!
“Triangles are not always right (although they are never wrong)” - Khan Academy
Hehe I like that
that 'right' means the right angle, right?
@@jason_mi1k_lee right
@@RummanNaser I didn't know until I watch the video that "right" (American) translates to "Right-angled" (English).
I guess you never stop learning.
diagram not to scalene triangle ~not khan academy
As long as the two sides of length 4 are equal the answer will be the sum of the other two sides. Take the drawing from 2:52 and slide the side of length 4 down like you did at 1:30t o form a rt triangle whose sides are 4 and 8. If you draw the remaining two sides of length 4 and x, you have a sort of diamond that can be split down the middle, into similar triangles: the two sides of length 4 match and the right angles match, and so the side of length x matches the side of length 8.
I guess the "99 percent" in the title is "not to scale" either... :P
We should all thank him for teaching us to pay more attention to the diagram not to scale
No, we should all resent him for giving a deceptive problem. That goes beyond "is not drawn to scale."
@@robertveith6383 "deceptive" assuming that the height equals 3 is the reason why everyone needed this lesson
@@robertveith6383 it was a mistake lol. Everyone makes mistakes, he clarified it.
For the original solve i also thought that the incorrect way might be incorrect because of the incorrect scales. But you can easily shift it into a Kite and then it is easily solved by symmetry. Not so easy on with 3 instead of four because you have to actually use pythagoras but still pretty straight forward. Nice Puzzles.
>trying to solve with trigonometry
>cant
>"ok, ill just move these two lines"
>answer becomes obvious
but don't give it .
I just added 5 + 3 = 8 and then we get a right triangle then use Pythagorean theorem and find x
I didn't move the lines. I just saw, that the "4" line segment can be divided in 3:5 ratio
When the test says "Solve for X" and then purposely shows the wrong diagram, they might as well just show a picture of a honey baked ham.
The diagram is not wrong. The diagram shows measurements you're supposed to use (lines with dimensions) and lines that are meant to be perpendicular (the symbol). It was never meant to be a tool to measure everything. It does serve its purpose properly. As it's somewhat my field (construction, architecture and the like), I can say that the constraints are set properly and there is one solution that does work universally. The issue was that many people assumed proportions were proper and they tried to find a solution that was not following the constraints given.
LOL
Plus, I was thinking this is solvable simply in your head, and not needing a square root table or SINE, TANGENT, COTANGENT tables.... This is not math, this is DECEPTION on part of lamo MIND YOUR DECISIONS>
@@yousurf374 all you need is Pythagoras rule and a bit of logic. You don't need to collapse the square root to know if you're right
@@europpe if you left the answer as squarer root of X, as the answer, you would be marked UNSOLVED... as the basis is in real numbers. I solved the original one, where he says proof method would be wrong, or less correct. IT was correct, regardless of his MORE correct method, as given... It was a whole number solution.
Now, my issue was that he did not state answer can be yielded as want for square root of a number, or that calculator could be used, with a square root function. Regardless of being able to get there without a calculator.. I get that part, but he did not fully solve this second iteration. My Advanced statistics professor would have given him a zero for the solution and even no partial for his solution/math method... as he did not fully solve. He was a harsh professor. I feared a question answer on a final exam as possibly being wrong, that I had erased the entire thing, as he marked number correct vs. number of questions asked... his final had only 8 questions, so I tried to increase my final score by removing it.... but later found out I was actually correct and should have left the math and final answer.. I had doubts that got the better of me... he caused me ANXIETY!!!! LOL.
@@yousurf374 no. If you solved the question using the method that was shown as incorrect in this video then there was a fundamental mistake in your assumptions. The fact it actually leads to the correct number is a coincidence caused by an unlucky choice of variables.
When i see how you solve it i remember i learned this all in school 30 yrs ago, but it does not come in my mind without looking how you solve it.
After watching the video i think it is easy.
But when you learned something and do not use it for 30yrs it is fully normal to forget about it ...........
My take (from my head, not written) was to add lines to prolong the 5 (right) and 3(outer left) with 3 and 4 (center) until it joined to form a triangle
Correct answer: The title should be ' 'Here's a deliberately misleading problem see if you can work out why'.
Bingo ... you nailed it!
This is the kind of BS that really weak teacher's use to "appear" smart to their students.
@@leahcasey2678 Not really, this teaches critical thinking. Like if you see "diagram not to scale" why would you assume the enclosure forms a perfect rectangle?
Heck even if the diagram looked super super close to being the same length, how do you know there isn't a .1 degree difference in the angles which would throw off your answer (without working out the geometry first)
A student shouldn't feel "tricked" if they get this wrong, they should realize they made assumptions that weren't true. Cause you know doing that in the real world is what gets you in deep poo poo.
@@leahcasey2678 This illustrates an important point of mathematics; you can't trust that something is so just because you assume it is so. There are many cases where mathematicians have demonstrated hundreds of thousands of cases where their theorem is correct and they cannot find a case where it is not, but they cannot prove it using pure mathematical logic and thus it is as "good" as any random statement.
@Mike L @Vesa E but we are to assume the diagram is on a flat two dimensional surface?
@@myclamish If this is a teaching moment, then they have to make it clear from the start the lesson is about just that. Because it looks like a geometry lesson. Had it been a trig lesson, maybe the student would have tried more trigonometry-centered solutions. You're right, we shouldn't assume things in mathematics, and it's an important lesson. But the teacher is resonsible for pointing that out. A "gotcha" math problem teaches nothing and only serves to frustrate a student.
I took a different approach at it (which might seem more difficult)
once you find that the hypotnuse for the first triangle is length 5, you can notice that it creates an isoceles triangle with the base as the hypotnuse for the bigger triangle (if that makes sense), next you find the angle which is 90 + sin^-1(3/5) (i know, its unnecesarily complicated) and using the cosine rule you get a length of 80 which gives the correct x value
Its nice seeing a different method, I was pleasantly surprised!
+1, I comes this method to mind at first, though it is a little brutal not elegant
This instruction in method will be very helpful. There are many problems that can use this intelligent de-construction. Thank you!
In the original task, moving two straight lines (4 units and 3 units) in parallel results in a kite. The two short sides of it are 4 units long, one of the long ones is 8 units long. Consequently, the other long side must also be 8 units long.
I would draw an extra line from the 4-4 vertex to the 8-8 vertex and call it two right triangles just because more people can understand right triangles. But yeah, obvious solution is obvious.
And here I thought I knew this stuff. Thank you for this humbling experience.
Damn, that triangle even changes it side lengths in the video from start to end.
The impossible right angle marked on there is just unethical
My first approach : x = 9 I have used the 3-4-5- rule in a couple of right triangles
But proven wrong when I watched the video further. Good trick
In the 60's I took every Geometry Course available in High School, but was clueless now. Thanks.
?
I was grinning the moment i saw the wrong answer...it was exactly what I thought..
When you can't even figure out the wrong method...
hahha! pure comment bro!
Haha
I really liked the manipulations of the shape that you did. What program or app did you use to accomplish that?
Damn it! lol. Nicely done. I enjoy having my mental shortcuts pointed out.
Drawing the image out of scale with line segments longer than they actually are is a dirty trick.
Agree .
It's so disgusting! That shape is so freaking weird since.It is "not to scale"
As someone with a PhD in physics, I'd give this video a bit of a thumbs down. Every problem has a context and it is important to convey that clearly. The English language and the tools that we have developed to diagram problems always go along with a set of assumptions because as humans we tend to be imprecise in our communication. For instance, I am assuming that the sides are straight even though the author does not mention this. And it would be standard to assume that the author intends the left side to be assumed to be vertical and the top to be horizontal. The words "Diagram not to scale" is not as clear as "The bottom 2 points are not necessarily on a horizontal axis". Or, sometimes one would draw a dashed line slightly above the bottom left point and towards and meeting the bottom right point to clearly indicate that the 2 points might be assumed to be different. Otherwise, it is trickey and not math or science.
I also agree. It's an idiotic "test".
It's not a dirty trick. If you don't assess the validity of the information you think is available, you will reliably miss the solution. Whether malice from someone or not.
The image very misleading to be honest LoL
Yes, and when trigonometry is used it ignores the misleading nature of the image.
yup when its to scale the whole image changes
@@codibanks2315 The scale doesn't matter one bit, trigonometry doesn't need scale to find the solution, it just needs enough data.
@@martintaper7997 my brain is small don't confuse me xD
Thank you for the captions. I nulled two right angles to have a right triangle with sides of 4, 12, and X.
Took me a while but I finally got it by myself! Great problem and content!
Pausing at 3:53: The length of X is nothing because the shape you've drawn cannot exist. A right triangle with a hypotenuse of length 3 and another side with length 3 is impossible. One of the sides has been labeled with an incorrect length.
exactly
You’re right but that’s not the point of the problem
I'll assume you meant 2:53 because I can't figure out house to pause a video 5 seconds after it finishes.
But I still don't see a right triangle with two sides of length 3 that you describe. If you're talking about the two 3 lines on the left side at 2:53 then nothing in the diagram says those two lines form a right triangle.
I even sketched it up in Fusion 360 and it worked fine and gave me the correct answers for both versions of the problem.
As a crosscheck, you could consider this which doesn't consider the construction from bottom left horizontally to the junction of the 4 and 5 lines.
1) Start by adding your own construction line from bottom left to top right. Now, as before, slide the '4' length along to the top right vertex creating an overall triangle from the original "z" shape.
2) You now have two triangles based on the same base, (the current overall hypotenuse). They both have a side of length 4. They also both have a right angle in their upper left vertex. These two triangles have "Right Angle + Hypotenuse + 1 Other Side" congruency. The other two matching sides must therefore be the same length.
3) Just as you say, in sliding the line up in step 1) we created a side of length 3 + 5 =8. This is the equivalent to the side X in the other congruent triangle. Length X therefore is 8.
Lol, I just tried to do it fast and assumed it was drawn to scale.
Thank you for the captions. I added sides 3, 4, and 5, then nulled two right angles. This left me with a right triangle having sides that measure 4, 12, and X.
I tried for like 20 minutes, I got no where but I'm at least proud to say I didn't fall for the easy trap
"Diagram not to scale" literally means that the distances writetn in it are not equal to the actual drawing.
IT DOESN"T mean "angles are not correct in the drawing".
No it doesn’t. It is ‘not to scale’ I.e not a scalar drawing. If the angles were the same it would be the same shape just scaled down or up. I see your point but a ‘not to scale’ diagram doesn’t need the same angles or you could just work out the enlargement and figure out the final length.
I gazed and contemplated for 15-20 minutes at the initial question of this video. Thankfully I realized the fact that the easiest way to solve this one is to imagine the hypotenuse of the 4 and (3+5) right triangle and then relate it to the hypotenuse of the right triangle with legs 4 and x.
Using Pythagoras (GOUGU 😊) Theorem,
Initial case :
(x^2) + 16 = 80
x = 8
Thumbnail case :
(x^2) + 9 = 80
x = √71
The problem with an initial length of 4 was more interesting because, when answered correctly, 8 contained a hidden trap. It was also necessary to prove that the length of the vertical segment from the top of the lower right angle is 4. But she had another beautiful solution. We will complement the right angle with sides 3 and 4 to the rectangle and break the resulting structure into two equal right triangles (according to a common hypotenuse and legs 4). In one of them, the other leg is equal to 8. Therefore, the desired segment is also equal to 8.
It was the first version of the problem that I proposed at the Ivano-Frankivsk Regional Olympiad in Mathematics for 8th grade students in 2020. With many correct answers, only one student gave a complete solution (with a justification of length 4 for a vertical segment). Others fell into the laid trap, or did not solve the problem at all, because they had not yet learned the Pythagorean theorem. The solution I proposed was not seen by any of the participants.
I got 8 as well, i'm annoyed because I paused it as soon as the video started, solved it then played it to check my answer just to see him change one of the values. It was so frustrating but I was relatively confident in my answer due to how round of a number the answer was
At the age of 57 having not done much maths for 30+ years i did get the right answer!!!.....Yeah me!!!!....
yay !
gg
Snap.....it’s something to do with being 57, 😝
No offense sir but this is a 6th grade problem...
@@ilovehomies in which country
Real world example of that figure our country's flag 🇳🇵😂
The precise way to draw the Nepalese flag is actually written in the constitution and it’s far more complex than this. Numberphile has a video on it
Only Nepal has unique flag in the whole world!🤩 Other countries flag is rectangular in shape.
Yeah
Maybe not everyone noticed or thought about it, but the GRAPHIC ANIMATION is great!! 👍❤️
I got the answer in a much simpler way, using common sense. What this video said was "you're wrong because you got the answer in an easier way than me, look how complicated I can make this!"
You could also criticise how the incorrect proof is based on the (unproven) assumption that the line between the points (the bottom two at 2:08) will be parallel to x.
I'm a complex man. I see a math problem, I click
There are no imaginary parts, so a better definition is "real man" 😁
it took me 10s from graphic to know its 9
or am i wrong?
Poo in the loo 👳🏿💩🐮🇮🇳
I solved this problem using vector addition. I got an answer of 8.63 , almost the same as your answer.
Hi. Thanks for the amazing video. Also I have a question and appologies if it has been asked here before: I am trying to self teach math, especially algebra and i really dont know what book to start with. Lets say that my math knowledge is around high school level and i want a book that is suitable but at the same time challenging enough for me to grow, what would be you recommendation?
Many many thanks
Oh wow, I solved it in my head from the thumbnail and made the exact mistake he predicted ( essentially )...
Because the problem intentionally misleads people to using the wrong method, for whatever reason. To prove a point, I guess, but then this isn't a math problem. It's a logic problem featuring math
The way I thought to do it was to start, again, with the 3-4-5 triangle. Given all sides are known, you can employ trigonometric functions to find all angles inside it. Lets call the left one L and the right one R.
The given diagonals, lengths given as 3 and 5, are parallel as they're shown to be 90 degrees from each other. And they both intersect with lines (the leftmost line originally a 4 turned to 3 in the modified example, and the line of distance x we want to find) that we know are orthogonal. Quick geometry shows us that the bottom left angle and the top right angle sum to 90 given they're parallel and orthogonal counterparts. Lets call the bottom left angle B and the top right is 90-B.
If we turn the image into a trapezoid, and we know the too left angle and the two angles formed by the 3-4-5 triangle, and recognizing the relationship B and 90-B, we can use the angle sum property of a quadrilateral to determine the value for B.
Given B we can find the angle 90-B and then draw a line parallel to x at the bottom. We know the angle between X and the right most line and can inflect 5 into the x direction. And we can inflect the hypotenuse of the 3-4-5 triangle's side (length of 5) using the angle found as 180 - (90-B) - 90 - R into the x direction and sum the two to find X
You can also overlap the 4 with the 5, and you know if you follow a straight line over the 3, the length will be 5, that will make the undefined line sqrt(50)+4. Since the triangles overlap, you will have to use pytagoras. 1^2+2^2=5. and subtract sqrt(5) from( sqrt(50)+4) and you`ll have the answer.
Slightly different way to redraw two lines: Create the rectangle with sides 3 and 4 by moving them parallel wrt each other. The hypotenuse is then obvious
Brilliant...first word cane to my mind at the end of solution💯
Well I chose to solve this for a non-euclidean space since that wasn't specified, so the answer is 9.
That's like saying "well I choose to focus my exercise on my butt supporting muscles, which is why I sit on the couch all day". In this case you gain points for being a smart alec, but you don't actually improve your mathematics skills, which is the point of the exercise here.
in most of the non-euclidean spaces, the 3/4/5 rule is wrong. So in my opinion, if you truly want to solve it this way, you have to describe the properties of your space that give an answer equal to 9 in this problem. good luck
@@DinoDiniProductions Its more like saying "you give a purposely misleading question so I give a ridiculous answer" - and thats something I am very fond of. The whole video has the ring of "being a smart alec" to it, he should be able to take his own medicine.
I did it in my head by just using the thumbnail lol
What’s that
Thank you for teaching me new ways to solve problems😄
I solved this using similar triangles and Pythagorean theorem only, without moving the lines as Presh did in the video.
First, connect the bottom left corner (where the two lines of length 3 are connected) to the top right corner (where the end of the line whose length we want to calculate and the end of the line of length 5 meet).
Then, two right triangles are made, which are similar, cause they have the same angles. We can easily see that the scale factor is 3/5. If we set the base of each triangle as x and 4-x, we can find that x=3/2 from the scale factor.
So knowing the two sides of the right triangles, using the Pythagorean theorem, we can find that the hypotenuses of the triangles are 3*sqrt(5)/2 and 5*sqrt(5)/2 for the small and big triangles respectively.
Finally, we can do the Pythagorean theorem one final time to find the length of the line we want to find. One side is 3, the other side is the sum of the hypotenuses we found in the previous step, so 4*sqrt(5), so the third side turns out to be sqrt(71).
"We'll review your application and get back to you. Have a nice day."
"Sometime geometry problem are trickier than they look."
Me, who always gets barely passing grade, but solved this in correct way from thumbnail: **visible confusion**
Yea, I remember in high school my geometry teacher said “students who usually do really good in math wind up being back at geometry while the opposite is true...this is because geometry uses common sense.”
@@fosterwalrus8413 So I’m a math genius? I failed at geometry so many times and only managed to pass because my teacher decided to let me cheat because that was more than her paygrade
@@fosterwalrus8413 I attended a state math competition in 5th grade and placed 5th. It was divided into four categories, and I got 4/10 in the geometry part where you had to measure objects (without a ruler) and get within 30% of the specified unit. Everything else I scored almost perfectly on. 39/40 on the exam, the largest part of the competition, 10/10 on a mental math exact test, and 8/10 on a mental math estimation test. Geometry is probably the only reason I didn't place 1st or 2nd in the state.
AAAA, REDDIT MOMENT, ama right????????????????????????? HAAAAAAAHAHAHAHAAAAAAAAAAAAAAAAAAAAAAAAAAA
Great problem, (I got the NTS misdirection), and after much thought managed to solve it. The way I figured it out I think was more intuitive/ visually satisfying…?? - at least to me! Because it can all be done on the original diagram. It goes like this:
1 slide the 5 side to align with the 3 side (no rotation…)
2 Slide the 4 side to close the figure
3 We now have a 8-4-root 80 triangle
4 Job done
First, find the length from bottom left point to upper right. That's the hypotenuse of a triangle whose sided are 4 and 8. That's Sqrt(80). Using that number as the length of the hypotenuse of the upper left triangle and the measure of the side given (3 or 4), you can find x. If the left side is 3, the answer is sqrt(71). If the left side is 4, answer is 8.
I did this all mentally.
This video (without the previous) just ended up in my list, so I tried it, but took a slightly different path (probably already shown in other comments): the missing part of the triangle can be seen as half of a rectangle, so you end up with a trapezium with opposing right angles. This can be divided in two triangles with right angle, both with the hypothenuse of sqrt(80), giving the same results as in the video.
I think this is the simplest solution
As soon as you mentioned "incorrect proof", the thought that the 3/4 hypotenuse is not necessarily parallel to x popped into my head.
atn (3/4) + atn (3/4) ≠ 90
Nice quiz to check what you learnt after 10 years of school. :) As an engineer I know result is "computable", but didn't guess to put line along the snake.
I didn't see the older video. I could see that the two sides of length 3 in this video were clearly not to scale. When I made a rough scale drawing I could see that the corner between the sides of length 4 and 5 clearly would not form a rectangle with the other three points in the incorrect version of the proof. Knowing that, I found the long hypotenuse as shown at 2:15.
The second he mentioned the "wrong method" I knew it would be the exact way I solved it in the thumbnail
Same
I checked the heights before I did it the "wrong way".
If cosA=4/5, then the height on the left would need to be equal to 5cosA (which is 4) for the hypotenuse of the bottom 3-4-5 triangle to be parallel to x.
When I saw the first Problem I didnt think about whether the 5 from the first 3-4-5 right triangle was parallel to the top line. The second you switched the number 4 to a 3 I realized I made a mistake. I actually took about 10-ish minutes and to my surprise found the solution the exact way you showed.
the question shows left vertical line is 4. but when go to solving part, it change to 3. when this line keep as 4, then the "wrong" way becomes right.
For a moment I though I was a genius and then I watched this video which took of the dream of going to Cambridge!!
Oh, I expected me to fail. I didn't expect the thousand staircase diagram. That Is NoT a TriaNglE! ThAt is Not a ParalLel LiNe!
@@vapx0075 haha
: when you forget to move stuff around to make their problem 10 times easier. : normal people now you're getting around to it.
I hadn't watch the video as I was interested in seeing if I could solve it. I spent a couple hours on it suing only the information that was available. I made the post then started the video again when you threw out changing the side from 4 to 3. I knew the original geometry wouldn't be directly applicable. So I tested the same principle and came up with the answer for the side length of 3. Just watched the rest of your video and it's basically a similar solution. Interesting problem. Thx for posting.
Really one of the best channels! 👌👏👍
Here's an idea: either draw your diagram to scale, or don't draw it.
You should never assume two lines are exactly equal unless it is explicitly stated
Failed my exam after running out of time trying to draw a diagram with km on the y axes. Thanks for the advice guy. Jeez
If only life were to drawn to scale it would all be so much easier. If you go back and look at the diagram, you can see that the two lines labeled as 3 units are NOT to scale. Don't give up.
@@Ben.Pickett3
"with km on the y axes"
_"draw your diagram to *scale*"_
You could have used a 1:100 000 scale.
@@SWilliams2990 but then he used those lines and used them as if they're true in scale when he turned it to combine 3 and 5.
I remember that zigzag line from another video so i solved it pretty quickly.
when you have half the right angle at the lower position 5/4 with a vertical line to the top you will have e right angle point there the the right and the length for the square sides you can create between the 45degree diagonale of 5 is root 5. Is this correct?
Extend length 4 to left top corner, equilateral triangle of side 3,
Now consider length of big triangle formed, length will be 4+3=7, other is 5, and is a right angle triangle of length 7, 5, and hypotenuse x.
X= root square of 7 plus squire of 5.
49+25= 74
X=root 74=8.6
Too many times I’ve doubted my answer in a maths exam because my teacher drew the acute angle that I had to find as an obtuse angle just for the fun of it.
I'm an online physics tutor, and one of my Wyzant students once asked me a question that made ME doubt myself and do it a few times "just to make sure," because it had a coefficient of friction of 1.4!
Don't you just love it when you're told that you've got the right answer 'incorrectly'.
yea, thats a little discouraging, my maths teacher always said "You got it right, but your proof was a little different, heres a simpler/shorter/more conventional way". This shits not easy in any way and every bit of progress should be recognised and celebrated.
Looking at it again, this was a bad example. If the answer was able to be found in a way than it was expected, the answer isn't wrong, the proof is different. The updated question from the viewer shows what MYDs point better. In that case the answer derived from the same proof would be wrong.
@@PigeonSwag In college chemistry class, the dean of chem. was my teacher. We had a test to balance equations. One of my answers was counted wrong so I asked why. He said "You didn't go about it the right way." I asked if the answer was correct: yes. I asked if the steps followed and made sense: yes. I asked why it was wrong. His answer: "There's only one way I know how to do it, my way and you didn't do it my way." I said "If the answer is correct, the steps make sense and its not your way, then I found another way to do it and ought to get extra credit." He declined to answer.
Yes, you have to keep the same height which is 4 and redraw in scale, to get the correct answer.
i used almost a similar method by joining the two vertices and applying the properties of similar tringles, not showing off but easy problem for an average JEE aspirant
Before viewing the video, I created the drawing, starting with the side of length 4 on the left and the side on the right with length 5, cannot be 5, but should be longer, around 6.2 if "x" is supposed to be a straight line with a 90 degree angle on the left. So, diagram not to scale is the beginning and end of the problem. So let's see what the video says.
In the amount of time it's taken to show your work on this one question, you now have 10 minutes to finish the other 49 other math questions on the final exam, lol.
Why is this so relatable 😖😅
8.
Extend side 5 by 3 and connect with corner between 3 and vertical 4. The length of the connection is also 4, so x is equal 5+ 3 which is 8.
Vectors make this problem so much clearer to see than triangles.