A wire was bent into the shape of a rectangle with width 5 and length 7. If the same wire is bent into the shape of a square, what is the length of a side of the square?

The problem involves a wire bent into different shapes, and the length of the wire remains constant in both configurations. First, let's calculate the total length of the wire when it is bent into the shape of a rectangle.

### Step 1: Calculate the perimeter of the rectangle.
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2(\text{length} + \text{width})
\]
Here, the length is 7 and the width is 5, so:
\[
P = 2(7 + 5) = 2(12) = 24
\]
Thus, the total length of the wire is 24 units.

### Step 2: Use the same wire to form a square.
When the wire is bent into a square, the perimeter of the square must also be 24, since the length of the wire hasn't changed.

The perimeter \( P \) of a square is given by:
\[
P = 4 \times \text{side length}
\]
Let the side length of the square be \( s \). We can set up the equation:
\[
4s = 24
\]
Solving for \( s \):
\[
s = \frac{24}{4} = 6
\]

### Final Answer:
The length of each side of the square is 6 units.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What would be the side length if the wire had a different perimeter?
2. If the rectangle had a width of 4 and length of 6, what would the side of the square be?
3. What is the area of the square in this problem?
4. If the same wire is bent into a circle, what would be the radius?
5. What is the perimeter of a square with side length 10 units?

**Tip:** The perimeter of any shape is the total distance around it, and this remains the same even when the wire is bent into different shapes.

Learn how to calculate the side length of a square when a wire is first bent into a rectangle and then into a square. This geometry problem involves understanding perimeter concepts for both rectangles and squares. Suitable for students in Grades 6-8.

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