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Question
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
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Solution
Given sides of two sides are x cm and (x + 4) cm.
Sum of areas of two squares = 656 cm2
=> x2 + (x + 4)2 = 656 ...[∵ Area of square = s2 sq units]
=> x2 + x2 + 8x + 16 − 656 = 0
=> 2x2 + 8x − 640 = 0
=> x2 + 4x − 320 = 0
=> x2 + 20x − 16x − 320 = 0
=> x(x + 20) − 16(x + 20) = 0
=>(x + 20)(x − 16) = 0
=> x + 20 = 0 or x − 16 = 0
∴ x = -20 or x = 16
Hence x = 16 since the side of the square cannot be negative
x + 4 = 16 + 4 = 20
Therefore the sides of two squares are 16 cm and 20 cm.
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