Question

If the area of an equilateral trangle is 81root 3sqcm,find the length of its side.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{s}=\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{an}\mathrm{equilateral}△. \\ \mathrm{area}\mathrm{of}\mathrm{equilateral}△=81\sqrt{3}{\mathrm{cm}}^2 \\ \Rightarrow \frac{\sqrt{3}}{4}{\mathrm{s}}^2=81\sqrt{3} \\ \Rightarrow {\mathrm{s}}^2=81\times 4 \\ \Rightarrow \mathrm{s}=\sqrt{81\times 4}=9\times 2=18\mathrm{cm} \end{gathered}$$