Question

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

Answer 1

Given sides of two sides are x cm and (x + 4) cm.

Sum of areas of two squares = 656 cm²

=> x² + (x + 4)² = 656      ...[∵ Area of square = s² sq units]

=> x² + x² + 8x + 16 − 656 = 0

=> 2x² + 8x − 640 = 0

=> x² + 4x − 320 = 0

=> x² + 20x − 16x − 320 = 0

=> x(x + 20) − 16(x + 20) = 0

=>(x + 20)(x − 16) = 0

=> x + 20 = 0 or x − 16 = 0

∴ x = -20 or x = 16

Hence x = 16 since the side of the square cannot be negative

x + 4 = 16 + 4 = 20

Therefore the sides of two squares are 16 cm and 20 cm.