Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm2. Find the sides of the squares.
Area of a square = side × side
Given, squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm2
⇒ x2 + (x + 4)2 = 656
⇒ x2 + x2 + 16 + 8x = 656
⇒ x2 + 4x – 320 = 0
⇒ x2 - 16x + 20x - 320 = 0
⇒ x(x – 16) + 20(x - 16) = 0
⇒ (x – 16)(x + 20) = 0
⇒ x = 16, - 20
The sides are 16, 20.