Question

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

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

Answer 1

The correct option is B 24 cm

Given, area of an equilateral triangle $=16\sqrt{3}c{m}^2$
$\because$ Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(Side{)}^2$
$\Rightarrow \frac{\sqrt{3}}{4}(Side{)}^2=16\sqrt{3}\Rightarrow (Side{)}^2=64$
$\therefore$ Side = 8cm
[taking positive square root because side is always positive]
$\therefore$ Perimeter of an equilateral triangle = 3 $\times$ side = 3 $\times$ 8 = 24cm
Hence, the perimeter of an equilateral triangle is 24 cm.