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.
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).
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.
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.
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.
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.
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.
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.
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)
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
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
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
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.
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 😂
@@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.
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.
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).
@@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 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.
@@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.
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
@@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.
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.
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…
"Without a calculator" only if you can remember that the sine of 30 degrees is 0.5 but WITH that knowledge, eezie peezie.
@@scottmcshannon6821 Disagree! He defined it as a square and he is the one making the call.
SOHCAHTOA, possibly my favourite mathematical procedure, helped me. Not bad for a 50y.o.!
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.
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.
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.
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.
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.
I’ve been out of school too long and don’t want to think about it.
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.
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
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.
I dont know in which grade u all solve these but in India we learnt this around 7 th grade
Why not: Once it is determined that the triangle is a 45 45 90 then it follows that X = (8/Sin (45))/Sin (30)
Thank you
Area of triangle is 32, so s=4✔️2.
The triangle is a 30/60/90, so x=H=2s=8✔️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)
Sin30 = 0.5 so the x (hypotenuse) is twice the side of the square (2 x Sq root of 2
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
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)
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
Me too
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
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.
Position of those right angles shows it's a square
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.
got it D isos rt tri sq rt 32. 2 x = D thanks for the fun.
Oh dear --its the SQUARE of the hypotenuse --oops --60 years since I did this at school --bad memory --apologies !
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 😂
Option d is correct
D
So --64 = 16 + 16 ?
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.
d.)
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.
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).
You seem to have calculated the area of the square when what we're supposed to be calculating is length x.
@@gavindeane3670 Yes, you are right, so sorry. Thank you
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.
@@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.
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?
@@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.