Problem Solving

kwah wrote:Attached is a question from GMAT Prep Test #2.

What is the most efficient way of achieving the result?

Answer: D

Thanks,
K

Area of equilateral triangle, with each of the sides, t:



By Pythagoras Theorem, h² = t² - (t/2)² = t² - t²/4 = 3t²/4
h² = 3t²/4
h = t√3/2
Therefore, area of equilateral triangle = (1/2) * base * height = (1/2) * t * t√3/2 = t²√3/4

Area of square, with each side, s = s²

Now area of equilateral triangle and square are the same, so t²√3/4 = s²
So, t²/s² = 4/√3 or 4/3^(1/2)
t/s = 2/[3^(1/2)]^(1/2) = [spoiler]2/3^(1/4)[/spoiler]

The correct answer is D.