The area of an equilateral triangle is $36\sqrt{3}\text{ sq. cm}$. Find its perimeter.

Given:

Area = $36\sqrt{3}\text{ sq. cm}$

Let s be the side of equilateral triangle.

Area of equilateral triangle = $\dfrac{\sqrt{3}}{4} \times \text{side}^2$

$⇒ 36\sqrt{3} = \dfrac{\sqrt{3}}{4} \times s^2\\[1em] ⇒ 36\cancel{\sqrt{3}} = \dfrac{\cancel{\sqrt{3}}}{4} \times s^2\\[1em] ⇒ 36 = \dfrac{1}{4} \times s^2\\[1em] ⇒ s^2 = 36 \times 4\\[1em] ⇒ s^2 = 144\\[1em] ⇒ s = \sqrt{144}\\[1em] ⇒ s = 12$

Perimeter = 3 x side

= 3 x 12 cm

= 36 cm

Hence, the perimeter is 36 cm.