Question:
If the area of an equilateral triangle is $36 \sqrt{3} \mathrm{~cm}^{2}$, find its perimeter.
Solution:
Area of equilateral triangle $=36 \sqrt{3} \mathrm{~cm}^{2}$
Area of equilateral triangle $=\left(\frac{\sqrt{3}}{4} \times a^{2}\right)$, where $a$ is the length of the side.
$\Rightarrow 36 \sqrt{3}=\frac{\sqrt{3}}{4} \times a^{2}$
$\Rightarrow 144=a^{2}$
$\Rightarrow a=12 \mathrm{~cm}$
Perimeter of a triangle = 3a
$=3 \times 12$
$=36 \mathrm{~cm}$