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Question
Two squares have sides x cm and (x + 4) cm. The sum of their area is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.
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Solution
Given that, two squares have sides x cm and (x + 4) cm.
Sum of their area = 656 cm2
∴ x2 + (x + 4)2 = 656
x2 + x2 + 16 + 8x = 656
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, 16
But, x being side, cannot be negative.
So, x = 16
Thus, the sides of the two squares are 16 cm and 20 cm.
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