Question

If the area of an equilateral triangle is $24\sqrt{3}$ sq. m, then its perimeter is

• A. $96m$
• B. $12\sqrt{6}$ $m$
• C. $4\sqrt{6}$ $m$
• D. $2\sqrt{6}$ $m$

Answer 1

The correct option is B $12\sqrt{6}$ $m$

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

Given, area of the equilateral triangle $=24\sqrt{3}{m}^2$

$\therefore \frac{\sqrt{3}}{4}{a}^2=24\sqrt{3}{m}^2$

$\Rightarrow a^2=24\times 4$

$a=4\sqrt{6}m$

Perimeter of the triangle $=a+a+a=3a=3\times 4\sqrt{6}=12\sqrt{6}m$