Question:
If the area of an equilateral triangle is $36 \sqrt{3} \mathrm{~cm}^{2}$, find its perimeter.
Solution:
Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$
$\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=36 \sqrt{3}$
$\Rightarrow$ (Side) $^{2}=144$
$\Rightarrow$ Side $=12 \mathrm{~cm}$
Thus, we have:
Perimeter = 3 × Side = 3 × 12 = 36 cm