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.

Answer 1

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.