Question

Area of an equilateral triangle is given by $A=\frac{\sqrt{3}{a}^2}{4}$ where A is the area and $a$ is the side. Find the perimeter of the triangle if $A=16\sqrt{3}$ sq.cm.

Answer 1

Given that:

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

$A=16\sqrt{3}$ sq. cm.

Now,

$16\sqrt{3}$sq. cm.$=\frac{\sqrt{3}{a}^2}{4}$

$\Rightarrow a^2=64$ sq. cm.

$\Rightarrow a=8$ cm

Now, Perimeter of the equilateral triangle $=3a=3\times 8$ cm $=24$ cm