Question

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

• A. $48cm$
• B. $24cm$
• C. $12cm$
• D. $306cm$

Answer 1

The correct option is B

$24cm$

Explanation for the correct option:

Find the side of the equilateral triangle

It is known that the area of the equilateral triangle can be given as: $\frac{\sqrt{3}}{4}{a}^2$

Where a is the side of the equilateral triangle.

Since it is given that the area of the equilateral triangle is $16\sqrt{3}c{m}^2$.

So side will be,

$$\begin{gathered} \frac{\sqrt{3}}{4}{a}^2=16\sqrt{3} \\ \Rightarrow a^2=64 \\ \Rightarrow a=8cm \end{gathered}$$

Find the perimeter of the triangle

Since it is known that all sides of the equilateral triangle are equal.

So, the perimeter, $P$ of the triangle will be,

$P=8+8+8=24cm$

Hence, the correct option is (b) $24cm$.