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?

Answer: D

Thanks,
K
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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?

Answer: D

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

Image

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.
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by gmatmath » Fri Apr 06, 2012 7:45 am
The solution is attached .[/img]
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The area of an equilateral triangle.docx
solution
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