## GMAT Prep #2_PS Triangles and Squares #12

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### GMAT Prep #2_PS Triangles and Squares #12

by kwah » Sun Apr 01, 2012 6:45 pm
Attached is a question from GMAT Prep Test #2.

What is the most efficient way of achieving the result?

Thanks,
K
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GMAT Prep #2_PS Triangles and Squares #12.docx

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by [email protected] » Sun Apr 01, 2012 7:08 pm
kwah wrote:Attached is a question from GMAT Prep Test #2.

What is the most efficient way of achieving the result?

Thanks,
K
Area of equilateral triangle, with each of the sides, t: By Pythagoras Theorem, hÂ² = tÂ² - (t/2)Â² = tÂ² - tÂ²/4 = 3tÂ²/4
hÂ² = 3tÂ²/4
h = tâˆš3/2
Therefore, area of equilateral triangle = (1/2) * base * height = (1/2) * t * tâˆš3/2 = tÂ²âˆš3/4

Area of square, with each side, s = sÂ²

Now area of equilateral triangle and square are the same, so tÂ²âˆš3/4 = sÂ²
So, tÂ²/sÂ² = 4/âˆš3 or 4/3^(1/2)
t/s = 2/[3^(1/2)]^(1/2) = [spoiler]2/3^(1/4)[/spoiler]

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