Question

If the area of an equilateral triangle is $36\sqrt{3}{\mathrm{cm}}^2$, find its perimeter.

Answer 1

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2 \\ \Rightarrow \frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2=36\sqrt{3} \end{gathered}$$
$$\begin{gathered} \Rightarrow (\mathrm{Side}{)}^2=144 \\ \Rightarrow \mathrm{Side}=12\mathrm{cm} \end{gathered}$$

Thus, we have:
Perimeter = 3 × Side = 3 × 12 = 36 cm