The perimeter of the small square is one-third the perimeter of the large square. What are the side lengths of the squares?

small square side = x
large swuare side = x + 2

1;3

Let's solve the problem step by step:

Step 1: Let's assume the side length of the small square is x.

Step 2: The perimeter of the small square is given as one-third of 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 3 times that, which is 3(4x) = 12x.

Step 3: We know that the perimeter of the small square is one-third of the perimeter of the large square. Therefore, we can set up an equation:
4x = (1/3)(12x)

Step 4: Simplifying the equation, we have:
4x = 4x

Step 5: On both sides of the equation, x cancels out, resulting in:
0 = 0

Step 6: Since the equation simplifies to 0 = 0, this means that there are infinitely many solutions to this problem.

Step 7: In other words, there are infinitely many possible side lengths for both the small and large square that satisfy the given condition.

Therefore, we cannot determine the specific side lengths of the squares based on the given information.

To find the side lengths of the squares, we can set up an equation using the given information. Let's denote the side length of the small square as x, and the side length of the large square as x + 2.

The perimeter of a square is calculated by multiplying the length of one side by 4.

The perimeter of the small square would be 4 * x, and the perimeter of the large square would be 4 * (x + 2).

According to the given information, the perimeter of the small square is one-third the perimeter of the large square:

4 * x = (1/3) * (4 * (x + 2))

Now let's solve this equation step by step:

First, let's distribute the (1/3) into the parentheses:

4 * x = (1/3) * (4 * x + 8)

Now, let's distribute the (1/3) into the multiplication:

4 * x = (4/3) * x + (8/3)

To get rid of the fractions, we can multiply the entire equation by 3:

3 * (4 * x) = 3 * (4/3 * x) + 3 * (8/3)

This simplifies to:

12 * x = 4 * x + 8

Next, we can isolate the x term by moving 4 * x to the left side:

12 * x - 4 * x = 8

This further simplifies to:

8 * x = 8

Finally, divide both sides of the equation by 8 to solve for x:

x = 1

Therefore, the side length of the small square is 1, and the side length of the large square is 1 + 2 = 3.