A triangle has sides with lengths of 3, 5, and 4. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-31T09:03:03

#1#

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+5+4)/2=12/2=6#

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(6(6-3)(6-5)(6-4))#

#Area=sqrt(6(3)(1)(2))#

#Area=sqrt(6(6))#

#Area=sqrt36=6#

#Radius=A/s=6/6=1#