If the area of an equilateral triangle is
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