Question

If the area of equilateral triangle is 3$\sqrt{3}{cm}^2$ then find the height of equilateral triangle

Answer 1

Area of an equilateral triangle $=3\sqrt{3}$sq.cm

Let the side of the equilateral triangle be $a$cm

$\Rightarrow \frac{\sqrt{3}}{4}{a}^2=3\sqrt{3}$

$\Rightarrow a^2=12$

$\Rightarrow a=\sqrt{4\times 3}=2\sqrt{3}$

If the side of the triangle is considered as a base

$\Rightarrow$ Area of a triangle$=\frac{1}{2}\times$base$\times$height.

$\Rightarrow 3\sqrt{3}=\frac{1}{2}\times 2\sqrt{3}\times h$

$\Rightarrow h=\frac{3\sqrt{3}}{\sqrt{3}}=3$cm

$\therefore$ height of the equilateral triangle is $3$cm