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

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Answer 1 · 2016-07-24T08:12:09

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

If the sides of a triangle are $a$ $a$ , $b$ $b$ and $c$ $c$ , 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 $2.1$ .