Question

The radius of the incircle is $12$ cm and its area of the triangle is $144$ ${\text{cm}}^2$. Find the semi-perimeter of the incircle.

• A. $10$ cm
• B. $11$ cm
• C. $12$ cm
• D. $13$ cm

Answer 1

The correct option is C $12$ cm

Given, radius of incircle $=12$ cm, area of triangle $=144{\text{cm}}^2$

Radius of the incircle $=$ $\frac{\text{Area of the triangle}}{\text{semi-perimeter}}$
Therefore, semi-perimeter $=$ $\frac{144}{12}$
Thus semi-perimeter $=12$ cm