the perimeter of the small square is equal to one-half the perimeter of the large square,

write and solve the an algebric equation to determine what the side lengths of the square are.
small square is x
large square is x+2

P = 4x for small square

P = 4(x+2) for large square

4x+2 = 2(4x)

Solve for x then x+2.

To find the side lengths of the squares, we can write an algebraic equation based on the given information and then solve for the variables.

Let's denote the side length of the small square as 'x' and the side length of the large square as 'x+2'.

According to the given information, the perimeter of the small square is equal to one-half the perimeter of the large square.

The perimeter of a square is calculated by multiplying the side length by 4. Therefore, the perimeter of the small square is 4x, and the perimeter of the large square is 4(x+2).

So, we can write the equation as:
4x = (1/2) * 4(x+2)

Now, let's solve this equation:

4x = 2(x+2)
4x = 2x + 4
4x - 2x = 4
2x = 4
x = 4/2
x = 2

Therefore, the side length of the small square is 2 units, and the side length of the large square is 2 + 2 = 4 units.