A square and triangle share a side - what’s the longest side of the triangle?
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- Опубликовано: 24 мар 2024
- How to solve a geometry problem with a square and triangle. Learn more math at TCMathAcademy.com/.
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SOHCAHTOA, possibly my favourite mathematical procedure, helped me. Not bad for a 50y.o.!
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).
but we dont know its a square, that fact that hes assuming is irrelevant to the problem.
@@scottmcshannon6821 the video is called „a square and a rectangle“… So there is no need to assume anything…
The question should already say that is a square on the left without the teacher providing critical information mid-test.
there is nothing in the problem to prove that is a square. hes cheating.
@@scottmcshannon6821It actually says ... A SQUARE and a TRIANGLE, in the Title of the video !
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.
@@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.
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.
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.
I’ve been out of school too long and don’t want to think about it.
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.
Thank you
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
I dont know in which grade u all solve these but in India we learnt this around 7 th grade
Sin30 = 0.5 so the x (hypotenuse) is twice the side of the square (2 x Sq root of 2
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)
Area of triangle is 32, so s=4✔️2.
The triangle is a 30/60/90, so x=H=2s=8✔️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
This is what I got too
Position of those right angles shows it's a square
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
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.
I was taught 8 (hypotenuse ) is equal to the sum of the two opposite sides --simple --s =4 ----4 + 4 = 8 ?---
The square of the hypothenuse is equal to the sum of the squares of the opposite sides.
got it D isos rt tri sq rt 32. 2 x = D thanks for the fun.
Why not: Once it is determined that the triangle is a 45 45 90 then it follows that X = (8/Sin (45))/Sin (30)
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.
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
So --64 = 16 + 16 ?
Option d is correct
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)
D is the answer
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 😂
D
d.)
Oh dear --its the SQUARE of the hypotenuse --oops --60 years since I did this at school --bad memory --apologies !
a
That is an unsolvable problem. Nothing in the question says it's a square.
It actually says ... A *SQUARE* and TRIANGLE in the Title !
@@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.
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).
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.
there is no proof that that is a square, you are making unsubstantiated assumptions.
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
It actually says .. it is a square & a triangle, in the title!
@@MrSummitville thats just the headline, hasnt our modern news media taught you that all headlines are lies?
flawed question. it must explicitly state that it's a square. otherwise not enough info - unsolvable.
It is explicitly said in the first few seconds of the video.
@@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?
@@fredsmith6324It actually says, A SQUARE and a TRIANGLE in the title of the video. Can you read or not?
@@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.