Let's solve the problem step by step.

Step 1: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is: $P = 2 \times (\text{length} + \text{width})$ Here, the length is $7 \, \text{cm}$ and the width is $3 \, \text{cm}$. Plugging in the values: $P = 2 \times (7 + 3) = 2 \times 10 = 20 \, \text{cm}$

Step 2: Relating the perimeter of the square

The square has the same perimeter as the rectangle, which means the perimeter of the square is also $20 \, \text{cm}$.

The formula for the perimeter of a square is: $P = 4 \times \text{side length}$ Let the side length of the square be $s$. Then: $4 \times s = 20$

Step 3: Solve for $s$

Divide both sides of the equation by $4$: $s = \frac{20}{4} = 5 \, \text{cm}$

Final Answer:

The side length of the square is: $\boxed{5 \, \text{cm}}$

Let me know if you need further clarification!

Questions to Explore Further:

1. How do you calculate the perimeter of a rectangle with different dimensions?
2. What is the area of the square, given its side length?
3. What is the area of the rectangle in this problem?
4. How does changing the side length of the square affect its perimeter?
5. If a rectangle has twice the perimeter of a square, how do you find its dimensions?

Tip:

To quickly calculate the side length of a square when the perimeter is known, simply divide the perimeter by $4$.