Question

If the area of an equilateral triangle is 36$\sqrt{3}$ sq.m., Find its Perimeter.

Answer 1

Area of the equilateral triangle = $36\sqrt{3}\mathrm{sq}\mathrm{m}$
The area of an equilateral triangle is given by $\frac{\sqrt{3}}{4}(\mathrm{side}{)}^2$.
$$\begin{gathered} \mathrm{i}.\mathrm{e}.,\frac{\sqrt{3}}{4}(\mathrm{side}{)}^2=36\sqrt{3} \\ \Rightarrow (\mathrm{side}{)}^2=36\sqrt{3}\times \frac{4}{\sqrt{3}} \\ \Rightarrow (\mathrm{side}{)}^2=144 \\ \Rightarrow s\mathrm{ide}=12\mathrm{m} \end{gathered}$$

∴ Perimeter of the equilateral triangle = 3 × side
= 3 × 12 m
= 36 m