A triangle has sides with lengths of 4, 9, and 7. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-27T14:35:27

#Radius=(3sqrt5)/5#

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=(4+9+7)/2=20/2=10#

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(10(10-4)(10-9)(10-7))#

#Area=sqrt(10(6)(1)(3))#

#Area=sqrt(10(18))#

#Area=sqrt180=6sqrt5#

#Radius=A/s=(6sqrt5)/10=(3sqrt5)/5#