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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 ‘a’ cm and ‘b’ cm, respectively According to the question, 6a2 + 6b2 = 2328 Or, a2 + b2 = 2328/6 = 388 And, ab = 96 Using the formula,   x2 + y2 = (x – y)2 + 2xy 388 = (a – b)2 + 2 × 96 Or, (a – b)2 = 388 – 192 Or, (a – b)2 = 196 Or, a – b = ±14 So desired difference = 14 cm 

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