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Question

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm2. Find the sides of the squares.

A
12 cm and 16 cm
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B
16 cm and 20 cm
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C
10 cm and 14 cm
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D
6 cm and 10 cm
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Solution

The correct option is B 16 cm and 20 cmThe area of a square is side2 sq. units. As per the question, x2+(x+4)2=656 ⇒x2+(x2+8x+16)=656 ⇒2x2+8x−640=0 ⇒x2+4x−320=0 ⇒x2+20x−16x−320=0 ⇒(x+20)(x−16)=0 Thus, x - 20 or 16. But the side of a square can't be negative. ⇒x=16 and (x+4)=20. Thus, the sides of the two squares are 16 cm and 20 cm.

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