Question:
The area of an equilateral triangle is $36 \sqrt{3} \mathrm{~cm}^{2}$. Its perimeter is
(a) 36 cm
(b) $12 \sqrt{3} \mathrm{~cm}$
(c) 24 cm
(d) 30 cm
Solution:
(a) 36 cm
Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$
$\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=36 \sqrt{3}$
$\Rightarrow(\text { Side })^{2}=144$
$\Rightarrow$ Side $=12 \mathrm{~cm}$
Now,
Perimeter = 3 × Side = 3 × 12 = 36 cm