https://file.aiquickdraw.com/mathbot/file/1726106570260vofa029b.jpg

The image shows a problem regarding the formula for the perimeter of a rectangle, which is given as:

\[
P = 2(w + l)
\]

Where \(P\) is the perimeter, \(w\) is the width, and \(l\) is the length of the rectangle. The problem asks the following:

**Part a:**
- **Rearrange the formula** so that it is easy to determine the width when the perimeter is given and the length is known.
- Use the rearranged formula to solve for the width when the perimeter is 50 inches and the length is 7 inches.

### Let's solve this step-by-step:

1. **Rearrange the formula to solve for width \(w\):**

Starting with the original formula:
\[
P = 2(w + l)
\]

Divide both sides by 2:
\[
\frac{P}{2} = w + l
\]

Now, solve for \(w\):
\[
w = \frac{P}{2} - l
\]

This is the rearranged formula for width \(w\).

2. **Part b: Use this formula with given values:**
   - \(P = 50 \text{ inches}\)
   - \(l = 7 \text{ inches}\)

Plugging these into the formula:

\[
w = \frac{50}{2} - 7 = 25 - 7 = 18 \text{ inches}
\]

Thus, the width of the rectangle is 18 inches.

---

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How would you derive the formula for the area of a rectangle?
2. What would the width be if the perimeter was doubled but the length remained the same?
3. Can you solve for the length instead if the width is known and the perimeter is given?
4. How does the perimeter formula relate to other shapes, such as a square or triangle?
5. What happens to the width if both the perimeter and length are increased by 5 units?

**Tip:** When solving for a variable in a formula, always isolate the variable by performing inverse operations step-by-step.

Rearrange the formula for the perimeter of a rectangle (P = 2(w + l)) to determine the width for a rectangle with a perimeter of 50 inches and a length of 7 inches.

Learn how to rearrange the formula for the perimeter of a rectangle (P = 2(w + l)) to easily calculate the width when the perimeter is 50 inches and the length is 7 inches. This problem is suitable for middle school students and involves simple algebra and geometry concepts.

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