Find the Area of the Green Square in the right Triangle and Semicircle | Step-by-Step Tutorial

[iZAPMath]

PreMath, 👏👏 the use of colors and your diligence make it easy to understand! You Rock!! I've got an assistant, and you will smile! :)

[bentels]

Very nice. Simple enough if you're patient and methodical, but always good to see it explained well. 👍

[ShubhamSingh-tpdg]

This time, i am late!By the way, lots of love from INDIA

[math]

very well explained, love the challenge, thanks for sharing

[henrilaporte]

Left slope mL = (x - 7) / 7 . Right slope mR = - (x - 14) / 14 . Because both segments are perpendicular, mL*mR = -1 and we have same equation.

[piman]

Your solution doesn't seem to require the semi-circle (as we are told the green square is inside a right triangle), so can we assume there is another method of solution? Or maybe not be told the triangle is right-angled, and figure this out by using the semi-circle?

[harshuldesai]

Take on angle as x, the other one will be 90-x, this applies for all the triangle in the figure. So by AA all the triangles are similar to one another. Then take the biggest square's side length as y and you can easily solve a quadratic equation thereafter giving one of the solutions of it as 21. So 441 would be the answer. Nice problem!

[shahja]

I think we can solve it much easily after realizing that the triangle above yellow square is the same triangle above pink square. Since Both triangles have the same angle alpha and same angle beta, so, their opposite lengths are also same. So, the opposite of alpha angle above yellow square is x-7 = opposite side of the alpha angle above pink square which is 14., So, x-7=14 gives us x=21.

[johnhill]

Intuitively I thought x = 21, but I couldn't figure out how to prove it. I would have answered the question corrected, unless I had to show my work. Thanks!

[kiranbarnwal]

Series of similar right triangles and you are done!!

[ΚΑΝΑΒΟΣΜΑΝΩΛΗΣ]

6 secs by mind...no pen...Thanks for feeding our brains

[pinklady]

Amazing! I tried working out the puzzle before clicking on this thumbnail. It was *TOUGH.*

[thedarkknight]

Oh This Is Fantastic.Thank You Very Much Sir!

[philipkudrna]

Before watching: s=21, as 14/(s-14) = (s-7)/7 (by proportion of similar triangles), which leads to s=21 and the area being 441 square units.

[cengizerol]

The sum of the sides of the other two squares is equal to a green side.

[jamesmcgraw]

Isn’t the triangle inside the semicircle a 90 60 30 triangle?

[illyriumus]

I solved one of your questions for a change lol.

[bvwalker]

Technically x = 0 is a solution. It just means you only have the two other squares and no middle square.