Question

The sides of a triangle are $6cm,11cm$ and $15cm$. The radius of its incircle is:

• A. $\frac{5\sqrt{2}}{4}cm$
• B. $3\sqrt{2}cm$
• C. $6\sqrt{2}cm$
• D. $\frac{4\sqrt{2}}{5}cm$

Answer 1

The correct option is A $\frac{5\sqrt{2}}{4}cm$

We have : $a=6,b=11,c=15$

$s=\frac{1}{2}(6+11+15)=16$

Area of the Triangle, $\Delta =\sqrt{16\left(10\right)\left(5\right)\left(1\right)}=20\sqrt{2}c{m}^2$

Radius of the inner-circle $=\frac{\Delta }{s}=\frac{20\sqrt{2}}{16}=\frac{5\sqrt{2}}{4}cm$