Question

If the area of an equilateral triangle is $16\sqrt{3}{\mathrm{cm}}^2$, then its perimeter is
(a) 48 cm
(b) 24 cm
(c) 12 cm
(d) 36 cm

Answer 1

Given: The area of an equilateral triangle is $16\sqrt{3}{\mathrm{cm}}^2$.

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

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{an}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times x^2 \\ \Rightarrow 16\sqrt{3}=\frac{\sqrt{3}}{4}{\left(x\right)}^2 \\ \Rightarrow \frac{16\sqrt{3}\times 4}{\sqrt{3}}={\left(x\right)}^2 \\ \Rightarrow x^2=64 \\ \Rightarrow x=8\mathrm{cm} \\ \mathrm{Thus},\mathrm{Perimeter}\mathrm{of}\mathrm{triangle}=3x \\ =3\left(8\right) \\ =24\mathrm{cm} \end{gathered}$$

Hence, the correct option is (b).