Question

The area of an equilateral triangle is $81\sqrt{3}{\mathrm{cm}}^2$. Its height is
(a) $9\sqrt{3}\mathrm{cm}$
(b) $6\sqrt{3}\mathrm{cm}$
(c) $18\sqrt{3}\mathrm{cm}$
(d) 9 cm

Answer 1

(a) $9\sqrt{3}\mathrm{cm}$
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=81\sqrt{3}{\mathrm{cm}}^2 \\ \Rightarrow \frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2=81\sqrt{3} \\ \Rightarrow (\mathrm{Side}{)}^2=81\times 4 \\ \Rightarrow (\mathrm{Side}{)}^2=324 \\ \Rightarrow \mathrm{Side}=18\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Height}=\frac{\sqrt{3}}{2}\times \mathrm{Side}=\frac{\sqrt{3}}{2}\times 18=9\sqrt{3}\mathrm{cm} \end{gathered}$$