Question

The area of an equilateral triangle is $4\sqrt{3}$ cm². The length of each of its sides is

(a) 3 cm
(b) 4 cm
(c) $2\sqrt{3}$
(d) $\frac{1}{2}\sqrt{3}$ cm

Answer 1

(b) 4 cm

Area of the equilateral triangle = $4\sqrt{3}$ cm²

We know:
Area of an equilateral triangle = $\frac{\sqrt{3}}{4}{\left(\mathrm{side}\right)}^2$ sq. units
∴ Side of the equilateral triangle = $\left[\sqrt{\left(\frac{4\times \mathrm{Area}}{\sqrt{3}}\right)}\right]$ cm
= $\left[\sqrt{\left(\frac{4\times 4\sqrt{3}}{\sqrt{3}}\right)}\right]$cm = $\left(\sqrt{4\times 4}\right)$ cm = $\left(\sqrt{16}\right)$cm = 4 cm