Two squares have sides x cm and (x + 4)cm. The sum of this areas is 656 cm2. Find the sides of the squares.

#### Solution

The given sides of two squares = x cm and (x + 4) cm

The sum of their areas = 656 cm^{2}.

The area of the square = side × side.

∴ Area of the square = x (x + 4) cm^{2}.

⇒ Given that sum of the areas is 656 cm^{2}.

Hence by hypothesis, we have

⇒ x(x + 4) + x(x + 4) = 656

⇒ 2x (x + 4) = 656

⇒ 𝑥^{2} + 4𝑥 = 328 [dividing both side by 2]

⇒ 𝑥^{2} + 4c - 328 = 0

⇒ 𝑥^{2} + 20𝑥 - 16𝑥 - 328 = 0 [∵ By the method of factorisation]

⇒ 𝑥(𝑥 + 20) - 16(𝑥 + 20) = 0

⇒ (𝑥 + 20)(𝑥 - 16) = 0 ⇒ 𝑥 = -20 𝑜𝑟 𝑥 = 16

Case i: If x = 16; x + 4 = 20

∴ The sides of the squares are 16 cm and 20 cm.

Note: No negative value is considered as the sides will never be measured negatively.