Question

In an equilateral triangle of side $3\sqrt{3}cm$, find the length of its altitude.

Answer 1

Length of side = $3\sqrt{3}cm$

Area of equilateral triangle = $\frac{\sqrt{3}}{4}{a}^2$

Here $a=3\sqrt{3}cm$

$=\frac{\sqrt{3}}{4}\times (3\sqrt{3}{)}^2$

$=\frac{\sqrt{3}}{4}\times 9\times 3$

$=\frac{27\sqrt{3}}{4}$ sq. cm

Area of triangle = $\frac{1}{2}bh$

$\Rightarrow \frac{27\sqrt{3}}{4}=\frac{1}{2}3\sqrt{3}\times h$

$\Rightarrow \therefore h=\frac{9}{2}=4.5cm$