Question
In a right-angled triangle, the two perpendicular sides
are 9 cm and 12 cm. What is the radius of the incircle of the triangle?Solution
ATQ, Right triangle with legs a = 9, b = 12. Hypotenuse c = √(9² + 12²) = √(81 + 144) = √225 = 15. Area = ½ × 9 × 12 = 54. Semiperimeter s = (9 + 12 + 15)/2 = 36/2 = 18. In any triangle: Area = r × s, where r is inradius. So r = Area / s = 54 / 18 = 3 cm.
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