A square and an equilateral triangle have the same perimeter. What is

Question

A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the triangle to the area of the square?

(A)  \frac{9√3}{4}

(B)  \frac{2√3}{3}

(C)  \frac{4√3}{9}

(D)  \frac{2√3}{9}

(E)  \frac{√3}{2}

gmatophobia · Answer

Let the side of equilateral triangle = s

Let the side of the square = x

Given : 3s = 4x
s =  \frac{4}{3}  x

Area of equilateral triangle =  \frac{\sqrt{3} s^2}{ 4}

Area of square =  x^2

Required Ratio =  \frac{4\sqrt{3}}{9}

Option C

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