Question

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

Answer 1

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