Question

If the area of an equilateral triangle is $16\sqrt{3}c{m}^2$, then the perimeter of the triangle is

Answer 1

Given, area of an equilateral triangle $=16\sqrt{3}c{m}^2$
$\because$ Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(\text{Side}{)}^2$
$\Rightarrow \frac{\sqrt{3}}{4}(\text{Side}{)}^2=16\sqrt{3}\Rightarrow (\text{Side}{)}^2=64$
$\therefore \text{Side}=8cm$[taking positive square root because side is always positive]

$\therefore$ Perimeter of an equilateral triangle $=3\times \text{side}=3\times 8=24cm$

Hence, the perimeter of an equilateral triangle is $24cm$.