A square and triangle share a side - what’s the longest side of the triangle?

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  • เผยแพร่เมื่อ 18 ม.ค. 2025

ความคิดเห็น • 65

  • @Kleermaker1000
    @Kleermaker1000 3 หลายเดือนก่อน +1

    It's a 30-60-90 degrees right triangle, so hypotenuse X is twice as long as the side of the square. The diagonal in the square is the hypotenuse of both right triangles in the square, so 8^2 = 2a^2 => a^2 = 64 : 2 = 32 and a = square rt 32 = 4 x square rt. 2. So X = 2 x 4 x square rt. 2 = 8 x square rt. 2.

  • @philipkudrna5643
    @philipkudrna5643 9 หลายเดือนก่อน +6

    If d is the diagonal of a square, the height of the large triangle is d/sqrt(2). Since the righthand triangle is a 30-60-90 triangle, x is two times the height. This leads to 2*8/sqrt(2). Rationalising the fraction leads to 2/2*8*sqrt(2) or simply 8* sqrt(2) or answer d).

    • @scottmcshannon6821
      @scottmcshannon6821 9 หลายเดือนก่อน

      but we dont know its a square, that fact that hes assuming is irrelevant to the problem.

    • @philipkudrna5643
      @philipkudrna5643 9 หลายเดือนก่อน

      @@scottmcshannon6821 the video is called „a square and a rectangle“… So there is no need to assume anything…

    • @thomasharding1838
      @thomasharding1838 3 หลายเดือนก่อน

      "Without a calculator" only if you can remember that the sine of 30 degrees is 0.5 but WITH that knowledge, eezie peezie.

    • @thomasharding1838
      @thomasharding1838 3 หลายเดือนก่อน

      @@scottmcshannon6821 Disagree! He defined it as a square and he is the one making the call.

  • @jakemccoy
    @jakemccoy 9 หลายเดือนก่อน +6

    The question should already say that is a square on the left without the teacher providing critical information mid-test.

    • @scottmcshannon6821
      @scottmcshannon6821 9 หลายเดือนก่อน +3

      there is nothing in the problem to prove that is a square. hes cheating.

    • @MrSummitville
      @MrSummitville 8 หลายเดือนก่อน +2

      ​@@scottmcshannon6821It actually says ... A SQUARE and a TRIANGLE, in the Title of the video !

    • @richardhole8429
      @richardhole8429 7 หลายเดือนก่อน

      I read the title first, "a square and a triangle" and solved for x in my head in just a few seconds. The title is part of the presentation. If you missed that you could not solve the problem.

    • @jakemccoy
      @jakemccoy 7 หลายเดือนก่อน +1

      @@richardhole8429 The creator changed his title. That info was not there at the time of my original post. That proves that he knows he messed up. Also, if someone embeds/copies this video and shows it to a math class, the title will not show up. And we’re full circle back to my original post.

    • @richardhole8429
      @richardhole8429 7 หลายเดือนก่อน

      The guy does a great job of teaching. I am not perfect nor is he. Many enjoy his problems as a challenge and do not need or want the teaching portion and holler loud and long against it, picking faults over trivialities. I wish they would stop.

  • @c200d45e95
    @c200d45e95 5 หลายเดือนก่อน +1

    The square is not explicitly labeled as a square. You can't assume 45 based on a drawing (every geometry test I have ever taken says NOT TO SCALE). There should be hashes in the sides indicating congruity or explicitly state the 45 angle.

    • @gavindeane3670
      @gavindeane3670 4 หลายเดือนก่อน

      The video title says it's a square (although from some of the comments here it seems that the title didn't initially say that - apparently it's been edited to add that crucial point). But you're right - it's trivially easy to indicate on the diagram that it's a square, and he should have done so.
      It's quite common on this channel for the chalk board image and the video title not to be consistent - sometimes they even contradict each other.

  • @tombristowe846
    @tombristowe846 9 หลายเดือนก่อน +2

    Why is everyone rambling on about whether it's a square or not? The question is phrased "a square and a triangle share a side ". End of.

  • @matthewrippingsby5384
    @matthewrippingsby5384 9 หลายเดือนก่อน +2

    SOHCAHTOA, possibly my favourite mathematical procedure, helped me. Not bad for a 50y.o.!

  • @queredknight
    @queredknight 9 หลายเดือนก่อน +1

    I’ve been out of school too long and don’t want to think about it.

  • @c_b5060
    @c_b5060 9 หลายเดือนก่อน

    11:02 I would simplify. The height is X times the square root of one, the base is X times the square root of three, the hypotenuse is X times the square root of four.

  • @raghavsingh7034
    @raghavsingh7034 9 หลายเดือนก่อน +1

    I dont know in which grade u all solve these but in India we learnt this around 7 th grade

  • @thomasharding1838
    @thomasharding1838 3 หลายเดือนก่อน

    Since you defined that figure as a square, each side is equal to the square root of one half of the square of the diagonal or √((1/2)(8x8)) = √((1/2)(64) = √32 = √16x2 = 4√2. And since that side is the opposite side of a 30 degree angle of a right triangle, the hippopotamus will be twice the opposite, or 8√2.

  • @raya.pawley3563
    @raya.pawley3563 6 หลายเดือนก่อน

    Thank you

  • @joso5554
    @joso5554 9 หลายเดือนก่อน

    d) 8.sqrt(2)
    Because sin(30°)=0.5
    and sin(45°)=sqrt(2)/2
    So the common height of both triangles is
    8.sqrt(2)/2=x.0.5=x/2

  • @b213videoz
    @b213videoz 8 หลายเดือนก่อน

    x 8
    ---------- = -----------
    sin(45) sin(30)
    8 * sin(45) = x * sin(30)
    x = 8 * sin(45) / sin(30) = 11.313 which is the same as 8 * sqrt(2)
    Answer: D
    I'm AMAZED I was able to solve it.

  • @lesheinen6116
    @lesheinen6116 9 หลายเดือนก่อน +3

    Why not: Once it is determined that the triangle is a 45 45 90 then it follows that X = (8/Sin (45))/Sin (30)

  • @WilfParker
    @WilfParker 9 หลายเดือนก่อน

    Sin30 = 0.5 so the x (hypotenuse) is twice the side of the square (2 x Sq root of 2

  • @panagdimi
    @panagdimi 9 หลายเดือนก่อน

    The clown said: "So you don't need to know much geometry and algebra ...but obviously you DO need some geometry and algebra knowledge and skills to solve this". WTF !?!
    Then I skipped to the next video 😂

  • @warblerab2955
    @warblerab2955 9 หลายเดือนก่อน +1

    I didn't it different than the video. I figured out the sides of the square just like in the video. But after that, I used Trig. sin(30)= opposite(a side of the square)/hypotenuse. sin(30)= .5 Therefore hypotenuse = (4sqrt(2))/.5 which = 8sqrt(2)

  • @kennethwright870
    @kennethwright870 9 หลายเดือนก่อน

    Area of triangle is 32, so s=4✔️2.
    The triangle is a 30/60/90, so x=H=2s=8✔️2

  • @joukoniemi9250
    @joukoniemi9250 9 หลายเดือนก่อน

    X can´t be shorter than d (=8). It can´t be 8/square root 2. X=2xh (hight). h=d/square root 2. X=2xd/square root 2 = 2x8/square root 2 = 16/square root 2=11.3

  • @aaronbredon2948
    @aaronbredon2948 9 หลายเดือนก่อน

    No need to even solve the question to get the correct answer.
    Given that the square has an integer diagonal, the side must have a sqrt(2) element.
    The triangle is a 30-60-90 triangle, which means the hypotenuse is twice the short side, therefore x has a sqrt(2) element. The only answer with a sqrt(2) is D.
    But to solve, divide the diagonal by sqrt(2) to get the square side lengths of 4sqrt(2), then double to get 8sqrt(2).
    Or use the Pythagoras theorem 8²=a²+a² (the 2 short sides are equal). 64= 2a². 32=a². Sqrt(32)=a. Sqrt(16)×sqrt(2)=a. 4sqrt(2)=a. x=2a. 8aqrt(2)=x

  • @MrBobbybrown7
    @MrBobbybrown7 9 หลายเดือนก่อน +2

    I used the pythagorean theorem to find the length of the sides of the square which is SQR 32. Then I used the sine function to find that the length for x is about 11.313 or exactly 8 times SQR 2

  • @CarlWinter-oy8uf
    @CarlWinter-oy8uf 9 หลายเดือนก่อน

    I was taught 8 (hypotenuse ) is equal to the sum of the two opposite sides --simple --s =4 ----4 + 4 = 8 ?---

    • @francisdelpuech6415
      @francisdelpuech6415 9 หลายเดือนก่อน

      The square of the hypothenuse is equal to the sum of the squares of the opposite sides.

  • @btcsys
    @btcsys 8 หลายเดือนก่อน

    Position of those right angles shows it's a square

    • @gavindeane3670
      @gavindeane3670 4 หลายเดือนก่อน

      No it doesn't. The height of the "square" part could be one millimetre and the width 100 miles, and those right angles would still be right angles.
      The only thing that tells you it's a square is the video title.

  • @CarlWinter-oy8uf
    @CarlWinter-oy8uf 9 หลายเดือนก่อน

    So --64 = 16 + 16 ?

  • @CandiceJoergan
    @CandiceJoergan 9 หลายเดือนก่อน

    That is an unsolvable problem. Nothing in the question says it's a square.

    • @MrSummitville
      @MrSummitville 8 หลายเดือนก่อน

      It actually says ... A *SQUARE* and TRIANGLE in the Title !

    • @CandiceJoergan
      @CandiceJoergan 8 หลายเดือนก่อน

      @@MrSummitville Thanks for your input, mistaken though it may be. The title has been edited. In case you don't know what the word "edited" means, it means changed. You surely should have reasoned that after seeing some of the other comments.

  • @russelllomando8460
    @russelllomando8460 9 หลายเดือนก่อน

    got it D isos rt tri sq rt 32. 2 x = D thanks for the fun.

  • @CarlWinter-oy8uf
    @CarlWinter-oy8uf 9 หลายเดือนก่อน

    Oh dear --its the SQUARE of the hypotenuse --oops --60 years since I did this at school --bad memory --apologies !

  • @debendranathsamal2574
    @debendranathsamal2574 9 หลายเดือนก่อน

    Easiest way 1) p/d i=sin45=1/(root2), 2) p/x=sin30=1/2
    Deviding eq1with eq2,x will be equal to (root2xd)=(root 2*8)

  • @rajnityagi5538
    @rajnityagi5538 9 หลายเดือนก่อน

    Option d is correct

  • @TheDotBot
    @TheDotBot 9 หลายเดือนก่อน

    Realise that a 30/60/90 triangle is an equilateral triangle cut in half so the opposite is automatically half the hypotenuse, why even address the adjacent? It's irrelevant. You're making the simple and straightforward sound mysterious and arcane.
    Maths teachers really need to stop overexplaining things. It puts people right off mathematics as a subject.

  • @mouradbelkas598
    @mouradbelkas598 5 หลายเดือนก่อน

    Your solution is incorrect. I honestly don't understand why in the world you make things so complicated and complex. since the figure is a square and d=8, then 2s^2 = d^2 = 8^2, s = 4 and area i 16, not 8 x Sqrt(2).

    • @gavindeane3670
      @gavindeane3670 4 หลายเดือนก่อน

      You seem to have calculated the area of the square when what we're supposed to be calculating is length x.

    • @mouradbelkas598
      @mouradbelkas598 4 หลายเดือนก่อน

      @@gavindeane3670 Yes, you are right, so sorry. Thank you

  • @KayBeck-wn5lj
    @KayBeck-wn5lj 9 หลายเดือนก่อน

    D is the answer

  • @nancyfloyd7052
    @nancyfloyd7052 9 หลายเดือนก่อน

    D

  • @scottmcshannon6821
    @scottmcshannon6821 9 หลายเดือนก่อน

    there is no proof that that is a square, you are making unsubstantiated assumptions.

    • @raghavsingh7034
      @raghavsingh7034 9 หลายเดือนก่อน

      Hey.
      It's a square since we can proof it using congruency of triangle
      D is common
      Two sides are parallel because of 90 °
      So angles are equal
      Then by using ASA rule triangle are congruent
      Therefore opposite sides are equal and given angles is 90° so it's a square

    • @MrSummitville
      @MrSummitville 8 หลายเดือนก่อน

      It actually says .. it is a square & a triangle, in the title!

    • @scottmcshannon6821
      @scottmcshannon6821 8 หลายเดือนก่อน

      @@MrSummitville thats just the headline, hasnt our modern news media taught you that all headlines are lies?

    • @gavindeane3670
      @gavindeane3670 4 หลายเดือนก่อน

      ​@@raghavsingh7034You can't prove it's a square like that! We know it's a rectangle but we don't know from the diagram that it's a square.
      The only thing that tells us it's a square is the video title.

  • @kerrylittle7368
    @kerrylittle7368 9 หลายเดือนก่อน

    a

  • @mollymam7153
    @mollymam7153 9 หลายเดือนก่อน

    d.)

  • @fredsmith6324
    @fredsmith6324 9 หลายเดือนก่อน +1

    flawed question. it must explicitly state that it's a square. otherwise not enough info - unsolvable.

    • @francisdelpuech6415
      @francisdelpuech6415 9 หลายเดือนก่อน

      It is explicitly said in the first few seconds of the video.

    • @fredsmith6324
      @fredsmith6324 9 หลายเดือนก่อน +2

      @@francisdelpuech6415 not acceptable. it must be stated in text as part of the question, not during the explanation of how to do it. if it was presented on a test this way it would be unsolvable. i try to solve these before i listen to the video. i wasted 5-10 minutes trying to figure out how to do this without knowing for sure if it was a square before i gave up and listened. now i don't trust this guy. in what other questions is he going to add information during the video that you need to solve it?

    • @MrSummitville
      @MrSummitville 8 หลายเดือนก่อน

      ​@@fredsmith6324It actually says, A SQUARE and a TRIANGLE in the title of the video. Can you read or not?

    • @fredsmith6324
      @fredsmith6324 8 หลายเดือนก่อน

      @@MrSummitville i didn't notice that the title of the question states that it's a square. didn't think i'd have to look at the video title for information needed to solve a problem. he also states verbally during the video that it's a square. however, it must be written into the question. the question itself must contain all information needed to solve.

    • @gavindeane3670
      @gavindeane3670 4 หลายเดือนก่อน +1

      ​@@fredsmith6324You're absolutely right. It would have been extremely easy for him to indicate on the diagram that it's a square, and he should have done that.
      It's not uncommon on this channel for the chalk board image and the video title to be inconsistent. Sometimes they even contradict each other.
      Although in this case, according to some of the other comments the original video title didn't say it was a square either. Apparently the title's been edited to correct that error.
      I guess it's easier to edit the title than to edit the image, although there was a video recently where the image was incorrect and he updated it soon after posting.