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

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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...#