Question
In a right-angled triangle, the hypotenuse is 25 cm, and
one of the sides is 20 cm. Find the radius of the circle inscribed in the triangle.Solution
The third side of the triangle can be found using the Pythagorean theorem: x^2 + 20^2 = 25^2 x^2 + 400 = 625 x = √225 = 15 cm. The semi-perimeter (s) of the triangle is (15 + 20 + 25) / 2 = 30 cm. The area of the triangle is (1/2) * base * height = (1/2) * 15 * 20 = 150 cm². The radius of the inscribed circle (r) is Area / s = 150 / 30 = 5 cm.
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