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    Question

    In a triangle, the lengths of the sides are proportional

    to 4, 3, and 5. If the area of this triangle is 216 square centimeters, determine the triangle's perimeter.
    A 72 cm Correct Answer Incorrect Answer
    B 60 cm Correct Answer Incorrect Answer
    C 96 cm Correct Answer Incorrect Answer
    D 80 cm Correct Answer Incorrect Answer

    Solution

    Since, the sides of the triangle are in ratio 3:4:5, the given triangle is a right-angled triangle. Let the three sides of the triangle be '3x' cm, '4x' cm and '5x' cm, respectively So, area of the triangle = (1/2) X (3x) X 4x = 216 Or, 6x2 = 216 Or, x2 = 36 So, x = ±6 Since, length of side cannot be negative, x = 6 So, required perimeter = 6 X (3 + 4 + 5) = 72 cm Hence, option a.

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