Question

If area of an equilateral triangle is 3$\sqrt{3}$ cm², then its height is
(a) 3 cm (b) $\sqrt{3}$ cm (c) 6 cm (d) 2$\sqrt{3}$ cm

Answer 1

Let a and h be respectively the side and height of the equilateral triangle. Then
$$\begin{gathered} \frac{a^2\sqrt{3}}{4}=\frac{1}{2}\times a\times h \\ \Rightarrow \frac{a\sqrt{3}}{4}=\frac{1}{2}\times h \\ \Rightarrow a=\frac{2h}{\sqrt{3}} \end{gathered}$$
Therefore
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{1}{2}\times a\times h \\ \Rightarrow 3\sqrt{3}=\frac{1}{2}\times \frac{2h}{\sqrt{3}}\times h \\ \Rightarrow h^2=9 \\ \Rightarrow h=3\mathrm{cm} \end{gathered}$$
Hence, the correct option is (a).