Question

find the radius of the circle which is inside a right triangle whose sides are 5,4, 3 (explain with steps)

Answer 1

see the figure .
Let ABC is a right angle triangle.
where,
AB = 5 unit
BC = 4 unit
CA = 3 unit

Let centre of circle is O.
then,
area of ∆AOB + area of ∆BOC + area of ∆COA = area of ∆ABC
$\frac{1}{2}\times\:r\times\: (AB + BC + CA) =\frac{1}{2}\times\:3\times\:4\\\\r=\frac{4\times\:3}{5+4+3}\\\\r=1$

hence, radius of circle is 1 unit