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    Question

    The sum of the total surface areas of two cubes is 2328

    cm2. If the product of the length of their edges is 96 cm2, then find the difference (in cm) between the lengths of their edges.
    A 4 cm Correct Answer Incorrect Answer
    B 14 cm Correct Answer Incorrect Answer
    C 5 cm Correct Answer Incorrect Answer
    D 7 cm Correct Answer Incorrect Answer

    Solution

    Let the length of the edges of the two cubes be тАШaтАЩ cm and тАШbтАЩ cm, respectively According to the question, 6a2 + 6b2 = 2328 Or, a2 + b2 = 2328/6 = 388 And, ab = 96 Using the formula, ┬а x2 + y2 = (x тАУ y)2 + 2xy 388 = (a тАУ b)2 + 2 ├Ч 96 Or, (a тАУ b)2 = 388 тАУ 192 Or, (a тАУ b)2 = 196 Or, a тАУ b = ┬▒14 So desired difference = 14 cm┬а

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