Question

The area of an equilateral triangle is $(16\times \sqrt{3}){cm}^2$.Find the length of each side of triangle.

Answer 1

Area of equilateral triangle $=(16\times \sqrt{3})c{m}^2$

Area of equilateral triangle $=\frac{\sqrt{3}}{2}\times (side{)}^2$

$\Rightarrow$ $16\times \sqrt{3}=\frac{\sqrt{3}}{2}\times (side{)}^2$

$\Rightarrow$ $(side{)}^2=\frac{16\times \sqrt{3}\times 2}{\sqrt{3}}$

$\Rightarrow$ $(side{)}^2=32$

$\Rightarrow$ $side=\sqrt{32}$

$\Rightarrow$ $side=4\sqrt{2}cm$

We know that, all three sides are equal in equilateral triangle.

$\therefore$ The length of each side of equilateral triangle is $4\sqrt{2}cm$