# The sides of the triangle are 4cm, 13cm and 15cm. Calculate the radius of the circle around the triangle.

July 26, 2021 | education

| The radius of a circle circumscribed about a triangle can be found by the formula:

R = abc / 4S,

where R is the radius of the circumscribed circle, a, b and c are the sides of the triangle, S is the area of the triangle.

The area of an arbitrary triangle, for which all three sides are known, can be found by Heron’s formula:

S = √ (p (p – a) (p – b) (p – c)),

where p is the semiperimeter of the triangle.

p = (a + b + c) / 2;

p = (4 + 13 + 15) / 2 = 16 (cm).

S = √ (16 (16 – 4) (16 – 13) (16 – 15)) = √ (16 * 12 * 3 * 1) = √576 = 24 (cm square).

Substitute the known values into the formula and find the radius of the circumscribed circle:

R = 4 * 13 * 15/4 * 24 = 780/96 = 8.125 (cm).

Answer: R = 8.125 cm.