SOLUTION: A triangle has a perimeter of 96 m and an area of 138 sq m. What is the radius of the circle that is inscribed in this triangle?

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Question 940733: A triangle has a perimeter of 96 m and an area of 138 sq m. What is the radius of the circle that
is inscribed in this triangle?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of a triangle are tangent to the inscribed circle.
For each side,
the radius of the circle at the point of tangency is perpendicular to the side.
If we connect each vertex of the triangle to the center of the circle,
the triangle is split into 3 triangles.
Each of those triangles has a side of the original triangle as its base,
and the corresponding altitude is the radius, R of the circle at the point of tangency.

Adding the areas of those three triangles,
we get the area of the original triangle as
area=perimeter%2AR%2F2 .
In this case,
%2896m%29%2AR%2F2=138m%5E2
%2896m%29%2AR=2%2A138m%5E2
%2896m%29%2AR=276m%5E2
R=276m%5E2%2F%2296+m%22
R=highlight%2823%2F8%29m or R=highlight%282.875m%29