Question:
The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^{2}$. Its perimeter is
(a) 9 cm
(b) 12 cm
(c) $12 \sqrt{3} \mathrm{~cm}$
(d) $6 \sqrt{3} \mathrm{~cm}$
Solution:
(b) 12 cm
Area of an equilateral triangle $=\frac{\sqrt{3}}{4} a^{2}$ (where $a$ is the length of the side)
Thus, we have:
$4 \sqrt{3}=\frac{\sqrt{3}}{4} a^{2}$
$\Rightarrow a^{2}=16$
$\Rightarrow a=4 \mathrm{~cm}$
Perimeter of the equilateral triangle $=3 a=3 \times 4=12 \mathrm{~cm}$