Question

9. If the area of an equilateral triangle is 36​√3 cm², find the length of its side and its perimeter.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{an}\mathrm{equilateral}∆=\mathrm{s}\mathrm{cm} \\ \mathrm{Now},\mathrm{area}=36\sqrt{3}{\mathrm{cm}}^2 \\ \Rightarrow \frac{\sqrt{3}}{4}{\mathrm{s}}^2=36\sqrt{3} \\ \Rightarrow {\mathrm{s}}^2=36\times 4 \\ \Rightarrow \mathrm{s}=6\times 2=12 \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}=\mathrm{s}=12\mathrm{cm} \\ \mathrm{Now},\mathrm{perimeter}=3\mathrm{s}=3\times 12=36\mathrm{cm} \end{gathered}$$