Question

An equilateral triangle circumscribes a circle of circumference 16$\pi$ cm Find its perimeter (in cm)

• A. $32\sqrt{3}$
• B. $48\sqrt{3}$
• C. $64\sqrt{3}$
• D. $80\sqrt{3}$

Answer 1

The correct option is B $48\sqrt{3}$

Given, circumference of incircle $=16\pi$
$=>2\pi \times inradius=16\pi$
$=>inradius=8cm$
Inradius of an equilateral triangle of side $a$ is given by $\frac{a}{2\sqrt{3}}$
So, $8=\frac{a}{2\sqrt{3}}$
$=>a=16\sqrt{3}$ cm
And Perimeter of the equilateral triangle $=3\times 16\sqrt{3}=48\sqrt{3}$ cm