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    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?
    A 1 cm Correct Answer Incorrect Answer
    B 8 cm Correct Answer Incorrect Answer
    C 2 cm Correct Answer Incorrect Answer
    D 3 cm Correct Answer Incorrect Answer

    Solution

    ATQ, Right triangle with legs a = 9, b = 12. Hypotenuse c = тИЪ(9┬▓ + 12┬▓) = тИЪ(81 + 144) = тИЪ225 = 15. Area = ┬╜ ├Ч 9 ├Ч 12 = 54. Semiperimeter s = (9 + 12 + 15)/2 = 36/2 = 18. In any triangle: Area = r ├Ч s, where r is inradius. So r = Area / s = 54 / 18 = 3 cm.

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