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    Question

    In a right triangle, the sides are in the ratio 3:4:5. A

    circle is inscribed in the triangle. What is the area of the triangle covered by the circle? 
    A 6π cm² Correct Answer Incorrect Answer
    B 9π cm² Correct Answer Incorrect Answer
    C π cm² Correct Answer Incorrect Answer
    D 15π cm² Correct Answer Incorrect Answer

    Solution

    The triangle is a right triangle with sides in the ratio 3:4:5,  and the area is A = (1/2) × base × height  = (1/2) × 3 × 4 = 6 cm². The semiperimeter s = (3 + 4 + 5) / 2 = 6 cm.  The inradius r = A / s = 6 / 6 = 1 cm.  The area covered by the circle is πr² = π(1)² = π cm². Correct answer: c) π cm²

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