source: gmat prep from gmac exam

I couldn't post the pictures but you see 1) an equilateral triangle with sides of length T, and 2) an square showing right angles inside with side length S.

Question:
If the two regions have the same area, what is the ration of t:s?

A. 2:3
B. 16:3
C. 4 : sq 3
D. 2: 4th sq 3
E. 4: 4th sq 3

Correct Answer: D. 2 : 4th Sq. 3

can you please explain the answer? I couldn't get there.

ee 1) an equilateral triangle with sides of length T, and 2) an square showing right angles inside with side length S.

Question:
If the two regions have the same area, what is the ration of t:s?


Area of Eq Triangle = Area of Sq with length S

1/2*B*H= s^2
we need to find height for Triangle with length t. Drop a perpendicular bisector to find the height which is
t*sq(3)/2

1/2*t*t*sq(3)/2= t^2* sq(3)/4 -(1)
Area of Sq= s^2 -(2)'

(1)= (2) ---> Given

t^2*sq(3)/4= s^2

To find t:s,
t^2/s^2= 4/ sq(3)

t/s= sq(4)/sq(sq(3))

t/s= 2/ sq(3)^1/2
= 2/ (3)^1/2^1/2
= 2/3 ^1/4
= 2/ 4th root of 3

Thanks

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