Attached is a question from GMAT Prep Test #2.
What is the most efficient way of achieving the result?
Answer: D
Thanks,
K
GMAT Prep #2_PS Triangles and Squares #12
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Area of equilateral triangle, with each of the sides, t: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
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]
The correct answer is D.
Anurag Mairal, Ph.D., MBA
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The solution is attached .[/img]
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 solution
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