Calculate the Perimeter of the given shape | Side lengths are given as 9, 12, and 15
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- เผยแพร่เมื่อ 23 ธ.ค. 2022
- Learn how to calculate the Perimeter of the given shape. Simple and step-by-step explanation!
Today I will teach you basic tips and tricks to solve the given question in a simple and easy way. Learn how to find the perimeter of the square quickly and efficiently! . Step-by-step tutorial by PreMath.com
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Calculate the Perimeter of the given shape | Side lengths are given as 9, 12, and 15
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Po Shen Loh
Calculate the Perimeter of the given shape
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Good lesson math 👍👍👍 thanks 🙏👍
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My maths skills have atrophied somewhat decades after school so I actually enjoyed rediscovering how to calculate an amount like this using algebra.. thank you for the refresher.
Same here. Just revisiting as a hobby. I used to be pretty good at math but have been away from it for many decades.
"My maths skills have atrophied somewhat decades after school"
Since retiring my skills have dropped to a real number greater than zero and less than one.
This doesn't require algebra. Since it doesn't matter where the 12 length begins, align it with the end of the 9 length, and we have 15 by 9+12 and the perimeter is (15+21)x2.
I just made it into a rectangle. I moved the 12 unit segment to the top creating a 21 unit side. Then moved the smallest horizontal segment to the bottom creating another 21 unit side. Then moved all the small vertical segments to the right, creating a 15 unit side. Then added it up to 72.
It's been such a long time since I've studied math. This is very helpful.
Another way of visualizing it is to change the shape equivalently. Take the vertical segment middle right and move it leftward until it hits the vertical (15) segment on the left. This also pulls the vertical segment on the lower right leftward. By definition, the additional perimeter gained in the middle from the extension of the horizontal segments is lost on from the two horizontal segments on lower right, so the shape is equivalent.
Now you have a very simple shape:
+----- 9 -----+
| | A
| |
+----- 9 ----+
|
| B
||
+------------- 12 -----------+
| | C
| |
+------------- 12 -----------+
Where the left vertical is 15. A + B + C must also equal 15. So you have 15 + 15 + 9 + 9 + 12 + 12 = 72.
-Matt
another way is to make it rectangle)
Yes, pretty obvious. I worked it out in a few seconds from the thumbnail. Just slide the centre vertical to the left or right to simplify and then its 2 x (15 + 21) = 72
Wish I had thought of this method. You basically made his (and my) x variable zero. To move wall B in your graphic to the right to make x non-zero would have added perimeter length to the bottom rectangle but simultaneously subtracted the same perimeter length from the top rectangle. I got the right answer but took longer to figure it out.
It took me awhile but I did get the correct answer of 72 using the variable x the way you did but I complicated it unnecessarily by adding a variable for the indentation which I thought I needed to know. Then I noticed that no matter what value I used for x my result was 72. So I knew my answer without knowing the indentation length. Good brain test.
Slide the "12" line to the right so the "horizontal perimeter lines" are 9, 12, (9 + 12). Add the vertical perimeter 15 + 15.
Perimeter of shape = 9 + 12 + 9 + 12 + 15 + 15 = 72
That's how I did it.
Me too
Solved this one quite quickly. Formed an equation using algebra for the missing side lengths and one horizontal length cancels out. The vertical part of the perimeter simply equals 2 * 15. My answer is 72 and I hope this is correct ! Thankyou for your video.
Appreciate It!!
Excellent step by step explanation by an an excellent teacher. I am 72, retired and love your videos. Thank you
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That was excellent.
Wow....a much simpler solution than it first appears. 😲😲😲👏👏👏
you can make it rectangle moving sides and saving the perimeter.
let's just increase your x till 9, the shape becames L, then just move 12 side to the bottom.
the shape becames a rectangle with sides 15 and 9+12
Thanks
Gonna subscribe to this channel now. You reawakened the math in me, haha. I did it a little differently. I copied the thumbnail of your video. What I did was basically made the “visible” side under the 9 value ‘a’ and assigned the bottom wall as b. So basically I made an equation of 9 - a + 12 + b = ? And ended up a + b = 21 and then I substituted the ‘a+b’ in my total perimeter equation with a 21 and ended up with the same answer. Not quite as smart as yours but amazing how I ended up at the same conclusion. Man, I actually miss math class.
Thank you for the very nice explanation! It's always a pleasure to watch your very informative videos! :) Happy holidays. Greetings from Hungary.
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Great problem.
Good we help people to teach
Brilliant Yuusuf.
Brilliant Yuusuf ol' boy!
Thank u video 📹
Very nice.
My method: if this problem has a single answer, then that answer should work for any x (as you defined x). So I can assume x=9. And now the figure is pretty simple, L shaped, and you can see that it still comply with the constrains of the problem. Calculating its perimeter is trivial.
When you cancelled both Xs my mouth dropped. I've seen a flat image of the shape before and it made me hit play. Fantastic and concise explanation and solution.
I figured it out in my head before even starting to watch. Basically, the 2 unknown lengths equal 9. This holds true for any value of x.
Nice! Many thanks, Sir! 🙂
So nice of you, dear
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With that shape, the depth of the central part can be anything from 0 to 9, and the circumference will stay the same. So :
1 side of length 15, and the sum of the parallel sides is also 15 : total 30
Then, we have two segments of length 12, for a 24.
Finally, we have a segment of length 9 and the remainder also totals a length of 9, for a final 18.
30 + 24 + 18 = 72
Label the missing lengths a, b, c (vertical, from top down) and d, e (horizontal, from top down).
a + b + c = 15
d + e = 9 + 12
P = 15 + 9 + 12 + a + b + c + d + e
= 15 + 9 + 12 + 15 + 9 + 12
= 72
I got there by concluding this shape must be derived from a square with 15 sides. Missing chunk off the top is 6, and aligns with the portion of length 12. 12 - 6 gets you that extra bit, which is 6. 45 + 12 + 9 + 6 gets to 72 all the same.
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x = 9+12-y
x+y= 9+12
perimeter = 2(9+12) + 2×15
I'm big fan of your channel. Your clips made me a healthy hobby of solving math problems.
thanks for good lessons
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Did it in my head....
It's been a long, long time since I studied either Geometry or Algebra. It never occurred to me that we could calculate the perimeter without knowing the unmarked distances, or "solving for X"..
how about calc'ing the actual lengths of the missing sides? the overall perimeter value does not have much use.
It could be helpful to a painter who paints the entire exterior of a house.
This math problem is solved by thinking outside the box a bit, which is what makes it challenging. I admit it took me awhile.
The small horizontal section = y, the larger bottom section = X. Then 9+12-X = Y. So 9+12 = X+Y. So you have 15+15+2(9+12)
Thanks sir for amazing question and best solution 👍..😊
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Thanks for video.Good luck sir!!!!!!!!!
Thank you too
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Merry Christmas Professor!❤👍🍺🥂
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The perimeter is the sum of the absolute values of each piece. If x > 9 then the perimeter exceeds 72
At 1:30, the variable x has been introduced. The problem statement implies that the solution is the same for all values of x greater than 0 but less than 9. Outside that range, the figure would have a different shape. Similarly, the lengths of the 3 shorter vertical red line segments must each be greater than 0 and must add up to 15. So, let's first make x infinitesimally close to 9. The top two red line segments almost merge, end to end, into one line segment. Now, let's make the combined length of the almost merged line segments infinitesimally close to 0. The remaining short vertical line segment becomes almost 15 and the line segment of length 12 has moved up and is almost in line, end to end, with the segment of length 9, for a total length, if they were in line, of 9 + 12 = 21. Our figure becomes close to a rectangle with sides 15 and 21. For those who have been taught limits, the limiting case is that rectangle. The perimeter of the rectangle is 15 + 21 + 15 + 21 = 72, as PreMath found.
I agree. The method only works for values of x =< 9. For x>9 (where the figure would have a different shape as you say), the short, upper, unknown horizontal segment would algebraically be x-9, and x would not cancel out of the perimeter sum. For x>9, “9-x” from the example would have a negative length, which is not valid for a perimeter.
@@wsandell If this was only a word problem without a physical graph, then your logic would be correct. But since a physical figure has been shown, then x can never be 0 nor can it be greater than 9. In fact, x can only be 3 since it is physically 12 - 9.
Happy Christmas Premath and all at the channel
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Vertical lengths =15+15=30
Horizontal lengths =9+12 +9+12=42
Hence perimeter = 72
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Actually quite simple
I feel my method was similar. The side 9-x is the overlap of the sides with length 9 and 12. The side x+12 can also be denoted as 21-(9-x) as it would be the combined lengths of the two known horizontal lines minus their overlap(9-x). So the 9-x’s cancel out and you have 15+15+9+12+21=72.
All you have to do is see that if you move the horizonal edge 12 to the right until x becomes 9, you have increased the length of the bottom horizontal exactly the same amount as the horizontal you have lost by increasing x. The perimeter is now 2x15 + 2x(9+12) = 72. Took me ten seconds from the thumbnail.
@@garethhanby okay…congrats on taking 10 seconds on a simple question, I guess. Is there something you’re expecting me to say? I don’t really see our solutions being all that different conceptually. You did it more geometrically and mine was more algebraic but it was in essence the same move.
That was goat
I waa thinking of use trigonometrical reazons
Neat, we did it very similar though I labeled the side as r thus making the bottom 9-r+12. It all washes out in the end.
Put the upper left corner in the origo of a coordinate system. How far do you travel in the x direction to the right? Double these numbers, as you to return to the origo. How far do you travel down in the y direction? Double the numbers to return to the origo. Those are the numbers you´re searching for. Rgr
But that would mean that 9 - x = 0. The diagram would look like a 15 * 9 rectangle with a 12 inch bump out at the bottom right. I would assume that the diagram requires that 0 < 9-x < 9
Took me a second to visualize it after reading your comment. The perimeter value is true for the whole range of over 0 to 9. imagine top and bottom as two buildings joined by a sliver of plasterboard up until when the alcove is completely gone. Each increment that the bottom line increases by is the same amount lost inside the alcove.
@@Brian67588 but then that would not be one shape. There needs to be a non-zero area connecting the top and bottom areas. And, that area can not be 0 or 9 units wide
I think the point of this problem is that the x created out of the info missing is irrelevant in the end as it cancels out and we can still get the perimereter without thinking too much about that unknown side. You can give limits to the unkown side if you want, but it wont make a difference on the perimeter.
@@cesarrou123, by that reasoning, you can say that a triangle is just a quadrilateral where one of the angles is 180 degrees. The diagram in the question shows 8 lines joined at 90 degree angles. If the answer given were correct than we would actually only have 6 lines, which goes against the diagram. Or, it would be two closed rectangles connected by a line, which again would go against the diagram since it shows that that the area on the top is connected to the area at the bottom by an area in the middle.
@@sandydl2 we only care about the amount of lines and the shape of what we are talking about up until we define how are the sum of all it sides represented, once we get this equation where, as we see, this variable x which COULD turn the figure into a rectangle with a bump (again, you could point it out if this was on a test, and say it should never reach 0 so it stays true to diagram) cancels out and we get the perimeter independent of x.
Yay, I solved it.
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I wish my math skills are like your's
I found the answer in an unusual way (I Think).
I was never good at maths at school, in fact it was my worst subject, so I have always wanted to improve.
My total shot in the dark was to take the line with a value of 12 and move it up in position until superimposed over the line with a value of 9, I then subtracted 9 from 12 to to get the value of the line immediately underneath which was 3, I then subtracted that value of 3 from 9 to find the true value of 9, 3 and 12 which gave the bottom line a value of 18, I then added all these together plus the known value of 15 for the value on the right side of the shape and it came to 72.
Technically, with the given information, the small horizontal line is not necessarily 3. It can be represented as a variable (let's say X), however it doesn't actually matter what X is because you end up subtracting X from the total regardless. So your logic is mostly sound, but you just can't prove that X = 3.
Edit: In the video they actually represent that line as 9-X, using X for the blank distance shown by a dotted line, which is a weird way of doing it to me, but it all works out the same.
I'm good with visualization. Got it in my head pretty quick. I didn't use a variable. I simply moved the 12 length next to 9 and the overlap is the same as the extra little length. So it forms a 21×15 rectangle. But that's harder to see in your head.
Greetings from the BIG SKY. I guess I'm a sucker for a math problem.
You can simplify the problem by sliding the lower right formation to the right till you have eliminated the smallest horizontal segment. This won't change the perimeter as when the eliminated segment is reduced, the bottom segment increases. The answer is then easily seen.
That’s clever. I determined the short part you eliminated by calculating its length directly from the overlap of the 9 and 12 which is 3.
I love these things. I don't do any of the math, I just guesstimate the lengths and always come up with the right answer.
Did it in my head in under 10 seconds, but then again I regularly set out foundations, so this thind of stuff is second nature. find it hilarious when kids say"we'll never use that" in maths classes, mathematics is part of life.
If you "see" the geometry, then you see that as the depth of the "cup" increases, the bottom decreases by the same amount. Indeed, if x =9 (i.e., there is no cup) the perimeter is still 72. HOWEVER, it doesn't work if the "cup" is inverted (i.e., x > 9) because then, when the cup inversion increases the bottom ALSO increases by the same amount. So, again, "seeing" the figure, one could calculate the perimeter (72) without the cup, and then understand that the perimeter would not change no matter how you deepened the cup -- as long as you didn't invert the cup
ça parait compliqué et ça devient lumineux dès qu'on voit comment faire ;))
Easy...!
Merry happy and Godfull Christmass Sir!
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@@PreMath Also thank you for your hard work and that i can learn math in english because it was hard for me for the first step to learn math in english for reading etc. But because your hard work i can learn math words in english without any problems, but also please rest Sir, i am taking break from math in 24-26 days, spend this time good. Merry Chrisstmass Happy new Year and God bless.
Being pedantic, isn't the answer P >= 72 as x is unconstrained in the horizontal direction allowing the 'backtracking' line segment to reverse with an x > 9 leading to a potentially infinite perimeter? Or does the solver need to make a assumption?
Also whatever the overlap is of 12 and 9 will need to be taken out of the bottom line and will be the exact length of the other unknown "parallel" horizontal line.
I did it a different way: We have two unknown side lengths - the shorter indent (which I'll call x) and the longer bottom (which I'll call y). The perimeter is 15+15+12+9+x+y. We can see from the diagram that y=12-x+9. Rearranged, x+y=12+9. Substitute Into the equation: p = 15+15+12+9+12+9 = 72.
Cut the bottom side such that right side will be 12. Take the remaining portion to form upper rectangle. 2*(9 + 12 + 15) = 72 is the perimeter.
I just did 15 plus 15 then figured the two horizontal unmarked lines must add up to 9+12
So
15+15+9+9+12+12=72
I came to the solution slightly differently. I assigned the variable d to the short horizontal line and x to the bottom horizontal line. I came up with the equation:
X = 9 - D + 12 then simplified to X = 21 - D, then added +D to both sides and came up with X + D = 21.
Yep this is how I did it as well. Didn't know it would turn out that way when I started but it was neat that it did.
Yep. That works. You were able to isolate a single numerical value (21 for horizontal x 2) regardless of what your variables are.
what if you ever had to find X how would you do it ?
I did it a little bit different. I defined the space under the overhang as X so we have 15, 9, X, 12, (12+9-X) as our defined faces, and then the 3 unmarked sides sum to 15.
Same result,
I also read the problem as area first which was why it took me so long.
You don’t have to use algebra to figure this one out. The three sides adding up to 15 is mentioned. The portion of the side directly below the 12 unit side would be 12. The rest of the lower side would be some part of 9 units and the shortest horizontal side would be the other part of 9 units, due to all the angles being right and where the sides are aligned in reference to the known 9 and known 12.
I got 72 units, too!
Perimeter vertical = 2 * 15 = 30
Perimeter horizontal = 2 * (12 + 9) = 42
Perimeter total = 30 + 42 = 72
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about 72
Sir can you please make a video on the following question 🙏
A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be α and β respectively. Prove that the height of the house is h(1+tanα tanβ) metres.
Dear Yashveer, please keep in mind that there are many requests ahead of you. So please be patient. Thanks for asking. Cheers
@@PreMath Thank You so much sir 🙏
@yashveersingh1858 I calculate the height to be h(1+tanα/tanβ) not h(1+tanα tanβ)
What about the vertical line on the far right?? Perimeter = circumference?
Yes, Perimeter = circumference
Please watch the video, and you'll see that all the sides are accounted for! Thanks for asking. Cheers
The three vertical lines on the far right must add up to 15 units. There is no way to determine any individual vertical line other than the one they tell you. You don't need to know the length of those three unknown vertical lines. You just need the total, which is 15.
Yes perimeter and circumference are the same thing although circumference is used on circles. The perimeter is the total of all outer lengths of a shape.
I figured out the second half absolutely the wrong way. Just as both the left and right are 15 units in length, the top and bottom are also the same "X + 12" because the Y under 9 (called "9 - X" in the video) can be made 0 by adding half of Y to 9 and subtracting half of Y from 12, since having only right angles will make the shape stay proportional. 9 + 0.5Y = 12 - 0.5Y, subtract 0.5 Y to have 9 = 12 - Y, subtract 12 for -3 = -Y, flip for 3 = Y. Half of 3 is 1.5, so 9 + 1.5 = 12 - 1.5 = 10.5. Yes, that's just taking the average of 9 and 12, I didn't realize that until just then. Both halves make 21 for the top half, +21 for the bottom half of length for 42, +15 +15 gives 42 + 30 = 72.
Basically, I manually figured out that 9 - X + X +12 ultimately cancels out. But this way we're now doubly certain that X + 12 = 21, which means X = 9 and "9 - X" is the longest 0 I've ever seen.
I got 72 in my head. I stretched out the short line to be zero length which then meant the longest distance at the bottom was 9+12=21 So I got 21+21 = 42 and 15+15=30 so, 42+30= 72
Exactly. I did it the same way.
Is there a way of calculating how many units the bottom horizontal line? (Or middle horizontal line?) Thanks.
No; the values are indeterminate. All we can say is that the middle segment is between 0 and 9 units in length, with the bottom segment equal to 21-(middle segment length). So, if the middle segment was 2 units in length, the bottom would be 19 units.
@@staratmidnight7 I thought so but wasn’t sure. Thank you for responding.
I was trying to determine the indentation length before I realized that there is no way to know it. Once I gave up on that I got the answer quickly.
@@tykemorris That much I saw right away and would have felt bad if I was proven wrong. Algebraic formulas were never my strong point. Quite the opposite.
The way I thought about it, without using algebra, is that the bit of the perimeter opposite of 9 (the 9-x in your example) is an extra chunk in addition to the 9 and 12, whilst the bottom line (12 + x) is larger than 9 and 12 by the same amount, thus they cancel it. Basically the same math but a different way of considering it that is more visual.
Call the long unknown side X and the short unknown Y. X = 12 -Y + 9; so X + Y = 12 + 9…🙂
That’s the way I did it, but from top down, instead of bottom up.
I just imagined moving the 12 back so that we end up with a L shape the folded up to make a 21 x 15 rectangle with the same perimeter. Took all of 10 secs
12=a+b 》 P=2×15+2(9+b+a)=30+2(9+12)=30+2×21=30+42=72
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Providing x is between 0 and 9 the=perimeter will be the the same
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hahahaha Beautiful! 🙂
That’s very easy again.
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# ' 4O.
I still would had liked to had known what the values of those sides were to prove to the perimeter was correct.
Please circle ke related questions
Sure! More to come... Keep watching
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bro when did i become bad at maths again i was good when i was 18 but after 23 this geometry stuff doesn't come to me instantly. thanks comp sci degree
thanks for the video
I'll use a ruler and solve it way quicker 😎.
Perimeter = 15 + 9 + 12 + (12 + 9) + (15)
Perimeter = 72 units
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Very interesting sir!
Glad you think so!
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Solved this within 30 seconds by just looking at it.
I got it without watching video so that’s a double win
Solve for X.
72
You can also determine the actual value of x because 9 - x = 3, which means x = 6.
Interesting that we never solve for x.
Excellent video, my first thought was not enough information, of course I was absolutely wrong!
You are correct.....not enough information........
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