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      Question

      The sum of the total surface areas of two cubes is 1572

      cm2. If the product of the length of their edges is 99 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 8 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 = 1572 Or, a2 + b2 = 1572/6 = 262 And, ab = 99 Using the formula, ┬а x2 + y2 = (x тАУ y)2 + 2xy 262 = (a тАУ b)2 + 2 ├Ч 99 Or, (a тАУ b)2 = 262 тАУ 198 Or, (a тАУ b)2 = 64 Or, a тАУ b = ┬▒8 So desired difference = 8 cm┬а

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