Question

The area of an equilateral triangle is . Its perimeter is
(a) 36 cm
(b)
(c) 24 cm
(d) 30 cm

Answer 1

(a) 36 cm
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2 \\ \Rightarrow \frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2=36\sqrt{3} \end{gathered}$$

$$\begin{gathered} \Rightarrow (\mathrm{Side}{)}^2=144 \\ \Rightarrow \mathrm{Side}=12\mathrm{cm} \end{gathered}$$

Now,
Perimeter = 3 × Side = 3 × 12 = 36 cm