Question

A triangle has sides with lengths of 7, 9, and 7. What is the radius of the triangles inscribed circle?

Answer 1

Radius of inscribed circle is `2.098` or say `2.1`.

Explanation:

If the sides of a triangle are `a`, `b` and `c`, then the area of the triangle `Delta` is given by the formula

`Delta=sqrt(s(s-a)(s-b)(s-c))`, where `s=1/2(a+b+c)`

and radius of inscribed circle is `Delta/s`

Hence as the sides of triangle are `7`, `9` and `7`

`s=1/2(7+9+7)=1/2xx23=11.5`

and `Delta=sqrt(11.5xx(11.5-7)xx(11.5-9)xx(11.5-7)`

= `sqrt(11.5xx4.5xx2.5xx4.5)=4.5sqrt28.75=4.5xx5.3619`

And radius of inscribed circle is `(4.5xx5.3619)/11.5=2.098` or say `2.1`.