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    Question

    The ratio of the length, width, and height of a cuboid

    is 4: 3 : 5 and the sum of the lengths of all its edges is 144 cm. Find the total surface area of the cuboid.
    A 1620 cm² Correct Answer Incorrect Answer
    B 1026 cm² Correct Answer Incorrect Answer
    C 756 cm² Correct Answer Incorrect Answer
    D 846 cm² Correct Answer Incorrect Answer

    Solution

    Let the common ratio be x. Hence, the length, width, and height of the cuboid are 4x, 3x, and 5x respectively.   According to the question, 4 × (4x + 3x + 5x) = 144   x = 3 Hence, the surface area of the cuboid = 2 (4x × 3x + 4x × 5x + 3x × 5x) = 2x2 (12 + 20 + 15) =2×32×47 =9×94 =846cm2

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