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.

Answer 1

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.