Question

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

Answer 1

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

Given, area of the equilateral triangle $=144\sqrt{3}{cm}^2$

Thus $\frac{\sqrt{3}}{4}{a}^2=144\sqrt{3}{cm}^2$

$\to a^2=144\times 4$

$a=24cm$

Now, the perimeter of the triangle $=$ Sum of all sides $=a+a+a=3a=3\times 24=72cm$