Question

The area of an equilateral triangle is $16\sqrt{3}{m}^2$.what is its perimeter?

Answer 1

Area of equilateral triangle$=16\sqrt{3}{m}^2$

Let the side of equilateral triangle$=a$ m

Area of equilateral triangle$=\frac{\sqrt{3}}{4}{a}^2$

$\Rightarrow 16\sqrt{3}=\frac{\sqrt{3}}{4}{a}^2$

$\Rightarrow a^2=\frac{16\sqrt{3}\times 4}{\sqrt{3}}=64$

$\Rightarrow a=\sqrt{64}=8$m

$\therefore$ Side of equilateral triangle$=8$ m

Perimeter of equilateral triangle$=3\times$ side

Perimeter of equilateral triangle$=3\times 8=24$ m.

Hence, the perimeter of equilateral triangle is $24$ m.