Question

If the area of an equilateral triangle is $16\sqrt{3}c{m}^2,$ then its perimeter is

• A. $36cm$
• B. $24cm$
• C. $12cm$
• D. $48cm$

Answer 1

The correct option is B $24cm$

Given: Area of an equilateral triangle $=16\sqrt{3}c{m}^2$

$\because$ Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(side{)}^2$

$\Rightarrow \frac{\sqrt{3}}{4}(side{)}^2=16\sqrt{3}$

$\Rightarrow (side{)}^2=16\sqrt{3}\times \frac{4}{\sqrt{3}}$

$(side{)}^2=64$

$\Rightarrow \text{Side}=8cm$

$\therefore$ Perimeter of an equilateral triangle

$=3\times \text{side}$

$=3\times 8$

$=24cm$

Hence, $\left(b\right)$ is the correct answer.