Question

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

Answer 1

Step 1: Find the side of triangle​

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

Let $x$ be the side of an equilateral triangle.

We know that,
Area of equilateral triangle $=\frac{\sqrt{3}}{4}\times (\text{side}{)}^2$

$\Rightarrow 16\sqrt{3}=\frac{\sqrt{3}}{4}\left(x^2\right)$

$\Rightarrow x^2=\frac{16\times 4\times \sqrt{3}}{\sqrt{3}}$

$\Rightarrow x^2=64$

$\Rightarrow x=\sqrt{64}$

$\Rightarrow x=\sqrt{8\times 8}$

$\Rightarrow x=8$

Thus, side of triangle is $8$ cm.

Step 2: Calculate the perimeter of triangle​

Perimeter of triangle $=x+x+x$

$=8+8+8$

$=24$

Thus, perimeter of triangle is $24$ cm.

Hence, (b) is the correct answer.