Question

If the area of an equilateral triangle is $36\sqrt{3}{\text{cm}}^2$. Find the length of its side and perimeter.

Answer 1

Area of equilateral triangle$=\frac{\sqrt{3}}{4}\cdot sid{e}^2$

$36\sqrt{3}=\frac{\sqrt{3}}{4}\cdot sid{e}^2$ [given]

$\Rightarrow \frac{36\sqrt{3}\times 4}{\sqrt{3}}=sid{e}^2$

$\Rightarrow 36\times 4=sid{e}^2$

$\Rightarrow side=\sqrt{36\times 4}$

$\Rightarrow side=6\times 2$

$\Rightarrow side=12cm$

Length of its side $=12$cm

Perimeter of equilateral triangle $=3a$

$=3\times 12$

$=36$cm.