The area of an equilateral triangle is $4\sqrt{3}$ cm², its perimeter is :

1. 16 cm

2. 4 cm

3. 12 cm

4. 8 cm

Given,

Area of equilateral triangle = $4\sqrt{3}$ cm²

By formula,

Area of the equilateral triangle = $\dfrac{\sqrt{3}}{4}$ x side²

$\Rightarrow 4\sqrt{3} = \dfrac{\sqrt{3}}{4} \times \text{side}^2\\[1em] \Rightarrow \text{side}^2 = \dfrac{4 \times 4\sqrt{3}}{\sqrt{3}}\\[1em] \Rightarrow \text{side}^2 = 4 \times 4\\[1em] \Rightarrow \text{side}^2 = 16\\[1em] \Rightarrow \text{side} = \sqrt{16}\\[1em] \Rightarrow \text{side} = 4\text{ cm}.$

By formula,

Perimeter of equilateral triangle = 3 x side

= 3 x 4 cm

= 12 cm.

Hence, option 3 is the correct option.