The Area of a triangle is 80 cm^2, Perimeter is 8 cm, so what is the length of the radius of the inscribed circle?

Question

Choices:

A)5 cm

B)10cm

C)20cm

D)None of these

Answer 1

The triangle can be broken down into 3 smaller triangles--each small triangle has one of the 3 sides of the larger triangle, and perpendicular to each side will be a radius of the circle. So, if the 3 sides have lengths of a, b, and c, the area of each small triangle will be 0.5 ar, 0.5 br, and 0.5 cr, corresponding to the standard formula of 0.5 bh for the area of each triangle. The total area of the big triangle will then be

A = 0.5 (a + b + c) r

= 0.5 Pr, where P is the perimeter of the outer triangle.

In this problem, plug in the numbers and solve for r.

80 = 0.5 X 8 X r

r = 20, which corresponds to choice C