Question

The area of an equilateral triangle is 81$\sqrt{3}$ sq.m., Find its height.

Answer 1

Area of the equilateral triangle = $81\sqrt{3}\mathrm{sq}\mathrm{m}$
The area of an equilateral triangle is given by $\frac{\sqrt{3}}{4}(\mathrm{side}{)}^2$.
$$\begin{gathered} \mathrm{i}.\mathrm{e}.,\frac{\sqrt{3}}{4}(\mathrm{side}{)}^2=81\sqrt{3} \\ \Rightarrow (\mathrm{Side}{)}^2=81\sqrt{3}\times \frac{4}{\sqrt{3}}=324 \\ \Rightarrow \mathrm{Side}=18\mathrm{m} \end{gathered}$$

Side of the equilateral triangle = 18 m
Area of the equilateral triangle = $\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}$

$$\begin{gathered} \Rightarrow 81\sqrt{3}=\frac{1}{2}\times \mathrm{base}\times \mathrm{height} \\ \Rightarrow 81\sqrt{3}=\frac{1}{2}\times 18\times \mathrm{height} \\ \Rightarrow \mathrm{Height}=\frac{81\sqrt{3}}{9}\mathrm{m}=9\sqrt{3}\mathrm{m} \end{gathered}$$

∴ The height of the equilateral triangle is $9\sqrt{3}\mathrm{m}$.