Question

If the sides of a triangle measure $72,75$ and $21$. What is the measure of its inradius?

• A. $37.5$
• B. $24$
• C. $9$
• D. $15$

Answer 1

The correct option is C $9$

Given: Sides of a triangle are $72,75$ and $21$

Semi perimeter $s=\frac{72+75+21}{2}=84$

Area of triangle $=\sqrt{84\times 12\times 9\times 63}=\sqrt{\left(2{)}^4\right(3{)}^6(7{)}^2}=(2{)}^2\times (3{)}^3\times 7=4\times 27\times 7$

Now,

Inradius $r=\frac{△}{s}=\frac{4\times 27\times 7}{84}=9$

Hence, $9$ is the correct answer.