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

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 + 8x + 16 = 656

⇒ x2 + 4x – 320 = 0

⇒ x2 + 20x – 16x – 320 = 0

⇒ x(x + 20) – 16(x + 20) = 0

 

⇒ (x – 16)(x + 20) = 0

 

⇒ x = 16 cm

 

The other side = 16 + 4 = 20 cm

Answer 2

A/q

${x}^{2} + {(x + 4)}^{2} = 656 \\ {x}^{2} + {x}^{2} + 8x + 16 = 656 \\ 2 {x}^{2} + 8x + 16 - 656 = 0 \\ 2{x}^{2} + 8x - 640 = 0 \\ 2( {x}^{2} + 4 x - 320) = 0 \\ {x}^{2} + 20x - 16x - 320 = 0 \\ x(x + 20) - 16(x + 20) = 0 \\ (x - 16)(x + 20) = 0 \\ x - 16 = 0 \\ x = 1$

since length can't be in negative

therefore , x ≠ -20

so the length of one square is 16 cm and other is 20 cm.