Question

The length of each side of an equilateral triangle having an area of $9\sqrt{3}{\mathrm{cm}}^2$ is
(a) 8 cm
(b) 36 cm
(c) 4 cm
(d) 6 cm

Answer 1

Given: The area of an equilateral triangle is $9\sqrt{3}{\mathrm{cm}}^2$.

Let the length of the side of an equilateral triangle be x cm.

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{an}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times x^2 \\ \Rightarrow 9\sqrt{3}=\frac{\sqrt{3}}{4}{\left(x\right)}^2 \\ \Rightarrow \frac{9\sqrt{3}\times 4}{\sqrt{3}}={\left(x\right)}^2 \\ \Rightarrow x^2=36 \\ \Rightarrow x=6\mathrm{cm} \end{gathered}$$

Hence, the correct option is (d).