Question
The sum of the total surface areas of two cubes is 1452
cm2. If the product of the length of their edges is 103 cm2, then find the difference (in cm) between the lengths of their edges.Solution
Let the length of the edges of the two cubes be ‘a’ cm and ‘b’ cm, respectively According to the question, 6a2 + 6b2 = 1452 Or, a2 + b2 = 1452/6 = 242 And, ab = 103 Using the formula, x2 + y2 = (x – y)2 + 2xy 242 = (a – b)2 + 2 × 103 Or, (a – b)2 = 242 – 206 Or, (a – b)2 = 36 Or, a – b = ±6 So desired difference = 6 cm
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