Question

The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is

(a) 4:3 (b) 2:$\sqrt{3}$ (c) 4:$\sqrt{3}$ (d) none of these

Answer 1

Let the side be a.

Area of square = $a^2$

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

$\frac{\text{Area of square}}{\text{Area of equilateral triangle}}=\frac{a^2}{\frac{\sqrt{3}{a}^2}{4}}=a^2\times \frac{4}{\sqrt{3}{a}^2}=\frac{4}{\sqrt{3}}=4:\sqrt{3}$

Ratio is (c) $4:\sqrt{3}$