The area of an equilateral triangle is numerically equal to its perimeter. Find its perimeter correct to 2 decimal places.

Let the side of the equilateral triangle be a.

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

And, perimeter of equilateral triangle = 3 x side

It is given that the area of an equilateral triangle is numerically equal to its perimeter.

⇒ $\dfrac{\sqrt{3}}{4}a^2 = 3a$

⇒ $\sqrt{3}a^2 = 4 \times 3a$

⇒ $\sqrt{3}a^2 = 12a$

⇒ $\sqrt{3}a = 12$

⇒ $a = \dfrac{12}{\sqrt{3}}$

⇒ $a = \dfrac{12 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

⇒ $a = \dfrac{12\sqrt{3}}{3}$

⇒ $a = 4\sqrt{3}$

As we know perimeter of equilateral triangle = 3 x side

= 3 x $4\sqrt{3}$ unit

= 12 $\sqrt{3}$ unit

= 12 x 1.74 unit

= 20.78 unit

Hence, the perimeter of the triangle is 20.78 unit.