The area of an equilateral triangle is $144\sqrt{3} \text{ cm}^2$; find its perimeter.

Let the side of the equilateral triangle be a.

It is given that the area of an equilateral triangle is $144\sqrt{3}\text{ cm}^2$.

∵ As we know, the area of the equilateral triangle = $\dfrac{\sqrt{3}}{4} \times \text{side}^2$

⇒ $\dfrac{\sqrt{3}}{4} \times a^2 = 144\sqrt{3}\text{ cm}^2$

⇒ $\dfrac{\cancel{\sqrt{3}}}{4} \times a^2 = 144\cancel{\sqrt{3}}\text{ cm}^2$

⇒ $\dfrac{1}{4} \times a^2 = 144\text{ cm}^2$

⇒ $a^2 = 4 \times 144\text{ cm}^2$

⇒ $a^2 = 576\text{ cm}^2$

⇒ $a = \sqrt{576}\text{ cm}^2$

⇒ a = 24 cm

Now, perimeter of equilateral triangle = 3 x side

= 3 x 24 cm

= 72 cm

Hence, the perimeter of the triangle is 72 cm.