Question

The inradius of the triangle having sides $26,28,30$ units is

Answer 1

Answer: 8

$s=\frac{26+28+30}{2}=42$
$\Delta =\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
$=\sqrt{42\left(42-26\right)\left(42-28\right)\left(42-30\right)}$
$=\sqrt{42\times 16\times 14\times 12}$
$=\sqrt{\left(7\times 6\right)\times \left(4\times 4\right)\times \left(7\times 2\right)\times \left(6\times 2\right)}$
$=7\times 6\times 4\times 2$
$r=\frac{\Delta }{s}=\frac{7\times 6\times 4\times 2}{42}=8$