Question

The area of a circle inscribed in an equilateral triangle is $154c{m}^2$. The side of triangle is:

• A. $7\sqrt{3}$
• B. $14\sqrt{3}$
• C. $5\sqrt{3}$
• D. $10\sqrt{2}$

Answer 1

The correct option is B $14\sqrt{3}$

We have

$tan{30}^o=\frac{R}{\left(Side/2\right)}$

$\frac{1}{\sqrt{3}}=\frac{R}{\left(Side/2\right)}$ $(154=(22/7)\ast R^2)$

Therefore $Side/2=7\times \sqrt{3}$

$Side=14\times \sqrt{3}$