Question

The ratio of the area of a square of side a and that of an equilateral triangle of side a is

(a) 2 : 1 (b) 2 : $\sqrt{\text{3}}$ (c) 4 : 3 (d) 4 : $\sqrt{\text{3}}$

Answer 1

Area of the square = a²
Area of the equilateral triangle = $\frac{a^2\sqrt{3}}{4}$
$\frac{\mathrm{Area}\mathrm{of}\mathrm{square}}{\mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}}=\frac{a^2}{{\displaystyle \frac{a^2\sqrt{3}}{4}}}=\frac{4}{\sqrt{3}}$
Thus, the required ratio is 4 : $\sqrt{\text{3}}$.
Hence, the correct option is (d).