Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 sq. cm. Express this as an algebraic equation and solve it to find the sides of the squares.

Area of a square = (side)²

∴ Area of first square = x² and Area of second square = (x + 4)²

Given, sum of areas of two squares is = 656 cm²

∴ x² + (x + 4)² = 656

$\Rightarrow x^2 + x^2 + 16 + 8x = 656 \\[1em] \Rightarrow 2x^2 + 8x + 16 - 656 = 0 \\[1em] \Rightarrow 2x^2 + 8x - 640 = 0 \\[1em] \Rightarrow 2(x^2 + 4x - 320) = 0 \\[1em] \Rightarrow x^2 + 4x - 320 = 0 \\[1em] \Rightarrow x^2 + 20x - 16x - 320 = 0 \\[1em] \Rightarrow x(x + 20) - 16(x + 20) = 0 \\[1em] \Rightarrow (x + 20)(x - 16) = 0 \\[1em] \Rightarrow x + 20 = 0 \text{ or } x - 16 = 0 \\[1em] x = -20 \text{ or } x = 16$

Since, length cannot be negative hence x ≠ -20.

∴ x = 16 , x + 4 = 20.

Hence, the sides of two squares are 16 cm and 20 cm.