Question

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

Area of an equilateral triangle

$=\frac{\sqrt{3}}{4}\times (side{)}^2$ and its perimeter $=3\times$ side

Answer 1

Let each side of an equilateral triangle =x cm

$\therefore$ Its area $=\frac{\sqrt{3}}{4}(side{)}^2$

$=\frac{\sqrt{3}}{4}{x}^2=144\sqrt{3}\left(given\right)$

$\Rightarrow x^2=144\sqrt{3}\times \frac{4}{\sqrt{3}}$

$\Rightarrow x^2=144\times 4\Rightarrow x62=576$

$\Rightarrow x=\sqrt{576}=24cm.$

$\Rightarrow$ Each side =24 cm

Hence perimeter =3(24)=72 cm.