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

1.	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» 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.

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»

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.