# The sides of the triangle are 29 cm, 25 cm and 6 cm. Calculate the radius of the circle inscribed in the triangle.

July 24, 2021 | education

| The radius of a circle inscribed in a triangle can be found by the formula:

r = S / p,

where r is the radius of the inscribed circle, S is the area of the triangle, p is the semiperimeter of the triangle.

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

where a, b and c are the sides of the triangle.

p = (29 + 25 + 6) / 2 = 60/2 = 30 (cm).

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));

S = √ (30 (30 – 29) (30 – 25) (30 – 6)) = √ (30 * 1 * 5 * 24) = √3600 = 60 (cm square).

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

r = 60/30 = 2 (cm).

Answer: r = 2 cm.

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