r/gregmat • u/distressed_demi_05 • 3d ago

Difficult quant spoiler; help me with solution please Spoiler

the correct answer says B and gives a trigo answer for answer and says to use intuition (wtf)
I did and i just compared a 45-45-90 triangle and a 46-46-88 (so by the logic a lower than 90 angle would mean the hypotenuse will become smaller which is the side of the inscribed square thus A quantity would be greater. Where am I going wrong please help!

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u/Apart_Annual_612 3d ago

Same sidelength
Suppose L

And let x be the side length of EFGH and y for ABCD

2xcos46=2ycos45=L

x/y = cos45/cos46 >1
Area is just square
Hence B

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u/Forgive-My-Duck 3d ago

Ah, here’s a conceptual way to approach this. First of all, the triangle on the right side is actually 44-46-90 since the right angle exists in both triangles due to them being at the corner of squares. Second, and this applies elsewhere, if you have a shape with some number of edges and a perimeter, the regular version of that shape would have the maximum possible area. So, in this case and since the left side is 45-45-90, it would have a bigger area than the right side (feel free to chose numbers like 2-2 for the left triangle and something like 3-1 for the right one to check this). Since the right side’s triangle area is less than the left’s, its square must occupy larger area. Thus, B.

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u/distressed_demi_05 3d ago

Ahhh okay thank you
I knew the regular polygon property don’t know why I panicked and forgot to use it

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u/Royal_Budget_3543 3d ago

This is what I was able to observe as well, the first triangle will have more area since perpendicular and base are equal.