A triangle has sides with lengths of 4, 6, and 9. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-31T09:12:07

#Radius=1.006...#

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+6+9)/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(9.5-4)(9.5-6)(9.5-9))#

#Area=sqrt(9.5(5.5)(3.5)(0.5))#

#Area=sqrt(9.5(9.625))#

#Area=sqrt91.43=9.562#

#Radius=A/s=9.562/9.5=1.006...#