A triangle has sides with lengths of 3, 9, and 7. What is the radius of the triangles inscribed circle?

Question

1834 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-02T13:42:45

Radius of circle inscribed in a triangle#=A/s#

Where,

#A#=Area of triangle,

#s#=Semi-perimeter of triangle#=(a+b+c)/2# Note #a,b,c# are sides of the triangle

So,#s=(3+9+7)/2=19/2=9.5#

We can find the area of triangle using Heron's formula:
Heron's formula:
#Area = sqrt(s(s-a)(s-b)(s-c)) #

#rarrArea=sqrt(9.5(9.5-3)(9.5-9)(9.5-7))#

#Area=sqrt(9.5(6.5)(0.5)(2.5))#

#Area=sqrt(9.5(8.12))#

#Area=sqrt77.14=8.78#

#Radius=A/s=8.78/9.5=0.92...#