Area of a square = s²

Perimeter of a square = 4s

Let the sides of the square be a and b respectively.

Given, sum of the areas of two squares is 640 m² and the difference of their perimeters is 64m.

⇒ a² + b² = 640 and

4a – 4b = 64

⇒ a – b = 16

⇒ a = 16 + b

⇒ (16 + b)² + b² = 640

⇒ 2b² + 32b + 256 = 640

⇒ b² + 16b – 192 = 0

⇒ b² + 24b – 16b – 192 = 0

⇒ (b – 8)(b + 24) = 0

⇒ b = 8 m

Thus, a = 24 m