Question

Choose the correct answer of the following question:

Each side of an equilateral triangle is $6\sqrt{3}$ cm. The altitude of the triangle is

(a) 8 cm (b) 9 cm (c) $3\sqrt{3}$ cm (d) 6 cm

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{area}\mathrm{of}\mathrm{an}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times {\left(\mathrm{side}\right)}^2 \\ \Rightarrow \frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}=\frac{\sqrt{3}}{4}\times {\left(6\sqrt{3}\right)}^2 \\ \Rightarrow \frac{1}{2}\times 6\sqrt{3}\times \mathrm{Height}=\frac{\sqrt{3}}{4}\times 36\times 3 \\ \Rightarrow 3\sqrt{3}\times \mathrm{Height}=27\sqrt{3} \\ \Rightarrow \mathrm{Height}=\frac{27\sqrt{3}}{3\sqrt{3}} \\ \therefore \mathrm{Height}=9\mathrm{cm} \end{gathered}$$

Hence, the correct option is (b).