Question
The sum of the total surface areas of two cubes is 1512
cm2. If the product of the length of their edges is 113.5 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 = 1512 Or, a2 + b2 = 1512/6 = 252 And, ab = 113.5 Using the formula, x2 + y2 = (x – y)2 + 2xy 252 = (a – b)2 + 2 × 113.5 Or, (a – b)2 = 252 – 227 Or, (a – b)2 = 25 Or, a – b = ±5 So desired difference = 5 cm
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