A triangle has sides with lengths of 5, 8, and 3. What is the radius of the triangles inscribed circle?

1 Answer
SagarStudy
Jan 22, 2016

There exists no triangle with the given measurements because the given measurements form a straight line.

If you still want to calculate the are then I have explained below.

If #a, b and c# are the three sides of a triangle then the radius of its inscribed circle is given by

#R=Delta/s#

Where #R# is the radius #Delta# is the are of the triangle and #s# is the semi perimeter of the triangle.

The area #Delta# of a triangle is given by

#Delta=sqrt(s(s-a)(s-b)(s-c)#

And the semi perimeter #s# of a triangle is given by
#s=(a+b+c)/2#

Here let #a=5, b=8 and c=3#

#implies s=(5+8+3)/2=16/2=8#

#implies s=8#

#implies s-a=8-5=3, s-b=8-8=0 and s-c=8-3=5#

#implies s-a=3, s-b=0 and s-c=5#

#implies Delta=sqrt(8*3*0*5)=sqrt0=0#

#implies R=0/8=0#

Mathematically, since the area comes out to be zero therefore it proves that it is a straight line it is not a triangle, and since there is no triangle so there is no in-circle and thus no in-radius.

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