1 answer

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

Question:

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

Answers

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#.

.

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