Question

The area of an equilateral triangles is $2\sqrt{3}c{m}^2$, find the semi-perimeter.

Answer 1

If a equilateral triangle has side 'a' then its area$=\frac{\sqrt{3}}{4}{a}^2$

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

From the question $A=2\sqrt{3}$

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

$\frac{a^2}{4}=2$

$a^2=2\times 8$

$a^2=8$

$a=\sqrt{2\times 2\times 2}$

$=2\sqrt{2}$

For semi parameter

$=\frac{3a}{2}$

$=\frac{3\times 2\sqrt{2}}{2}$

$=3\sqrt{2}$cm.