Question

The area of an equilateral triangle is $(16\times \sqrt{3}){\mathrm{cm}}^2$. Find the length of each side the triangle.

Answer 1

It is given that the area of an equilateral triangle is $16\sqrt{3}$ 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
= $\left[\sqrt{\left(\frac{4\times 16\sqrt{3}}{\sqrt{3}}\right)}\right]$cm = $\left(\sqrt{4\times 16}\right)$cm = $\left(\sqrt{64}\right)$cm = 8 cm

Hence, the length of the equilateral triangle is 8 cm.