Question

Question 5
The length of each side of an equilateral triangle having an area of $9\sqrt{3}c{m}^2$ is

Answer 1

Given, area of an equilateral triangle = $9\sqrt{3}c{m}^2$
$\because$ Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(Side{)}^2$
$\Rightarrow \frac{\sqrt{3}}{4}(Side{)}^2=9\sqrt{3}$
$\Rightarrow (Side{)}^2=36$
$\therefore Side=6cm$
[taking positive square root because side is always positive]
Hence, the length of each side of an equilateral triangle is 6cm.