Let the sides of square be = x and y m. ATQ, x²+y²=640 -----------(1) 4x-4y = 64 x-y= 16-------------(2) (x-y)²= x²+y²-2xy 16²= 640-2xy 256-640 = -2xy 2xy = 384 ----------(3) (x+y)²= x²+y²+2xy (x+y)²= 640+384 (x+y) = √1084 x+y = 32 ------------(4) By eliminating (4) and (2) we get, x=24 and y= 8 So, sides of square are 24 and 8m

Problem Analysis:
Let's assume that the sides of the two squares are 'x' and 'y' respectively.

Step 1: Finding the Equations:
We can start by writing the equations based on the given information:
1. Sum of the areas of two squares = 640 m^2. So, we have the equation:
x^2 + y^2 = 640
2. Difference in their perimeters = 64 m. The perimeter of a square is given by 4 times the length of its side. So, we have the equation:
4x - 4y = 64

Step 2: Simplifying the Equations:
Let's simplify the second equation by dividing both sides by 4:
x - y = 16

Step 3: Solving the Equations:
We now have two equations:
1. x^2 + y^2 = 640
2. x - y = 16

We can solve these equations simultaneously to find the values of 'x' and 'y'.

Step 4: Substituting and Solving:
From equation 2, we can express x as y + 16 and substitute it into equation 1:
(y + 16)^2 + y^2 = 640

Expanding the equation:
y^2 + 32y + 256 + y^2 = 640

Combining like terms:
2y^2 + 32y + 256 - 640 = 0

Simplifying the equation:
2y^2 + 32y - 384 = 0

Dividing the equation by 2:
y^2 + 16y - 192 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula.

Step 5: Solving the Quadratic Equation:
Factoring the quadratic equation:
(y + 24)(y - 8) = 0

Setting each factor equal to zero:
y + 24 = 0 or y - 8 = 0

Solving for 'y':
y = -24 or y = 8

Step 6: Finding the Side Lengths:
Since the side length of a square cannot be negative, we discard the value y = -24 and consider y = 8.

Substituting y = 8 back into equation 2, we can find the value of x:
x - 8 = 16
x = 24

So, the sides of the squares are x = 24 m and y = 8 m.

Step 7: Final Answer:
The sides of the two squares are 24 m and 8 m respectively.