Question

If the sides of a triangle are $13,14,15,$ then the radius of the incircle is

• A. $\frac{65}{8}$
• B. $\frac{65}{4}$
• C. $4$
• D. $24$

Answer 1

The correct option is C $4$

Given: $a=13,b=14,c=15$
We know that $r=\frac{\Delta }{s}$
$\Rightarrow s=\frac{a+b+c}{2}=\frac{13+14+15}{2}=\frac{42}{2}=21$
$\Rightarrow \Delta =\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{21(21-13)(21-14)(21-15)}$
$\Rightarrow \Delta =\sqrt{21\times 8\times 7\times 6}=84$
$\Rightarrow r=\frac{84}{21}=4$