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    Question

    The sides of a triangle are 9 cm, 12 cm, and 15 cm. What

    is the area of the largest circle that can be inscribed in this triangle?┬а
    A 10 cm┬▓ Correct Answer Incorrect Answer
    B 15.42 cm┬▓ Correct Answer Incorrect Answer
    C 20 cm┬▓ Correct Answer Incorrect Answer
    D 28.26 cm┬▓ Correct Answer Incorrect Answer

    Solution

    The triangle is a right triangle. The area A = (1/2) ├Ч base ├Ч height = (1/2) ├Ч 9 ├Ч 12 = 54 cm┬▓. The semiperimeter s = (9 + 12 + 15) / 2 = 18 cm. The inradius r = A / s = 54 / 18 = 3 cm. The area of the inscribed circle is ╧Аr┬▓ = ╧А(3)┬▓ = 9╧А тЙИ 28.26 cm┬▓. Correct answer: d) 28.26 cm┬▓

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