https://file.aiquickdraw.com/mathbot/file/17254835078013darj6av.jpg

The image presents a problem involving a rectangle with a given perimeter and length. Let’s analyze and solve the problem step-by-step.

### Problem Analysis

The problem is about finding the width of a rectangle when the length and the perimeter are known.

**Given:**
- Length of the rectangle, \( l = 17 \) units
- Perimeter of the rectangle, \( P = 116 \) units

**Formula:**
The formula for the perimeter \( P \) of a rectangle is given by:

\[
P = 2l + 2w
\]

where:
- \( l \) is the length of the rectangle.
- \( w \) is the width of the rectangle.

### Solution

1. Substitute the given values into the perimeter formula:

\[
116 = 2(17) + 2w
\]

2. Simplify and solve for \( w \):

\[
116 = 34 + 2w
\]

\[
116 - 34 = 2w
\]

\[
82 = 2w
\]

\[
w = \frac{82}{2}
\]

\[
w = 41
\]

### Answer

The width of the rectangle is **41 units**.

Would you like further details on this solution, or do you have any additional questions?

### Related Questions:

1. How do you find the area of the rectangle using the length and width?
2. What would be the width if the length was doubled, keeping the perimeter constant?
3. How would the solution change if the perimeter formula was different?
4. Can we determine the length if only the perimeter and area are known?
5. How does the perimeter of a rectangle change with respect to its length and width?

### Tip:

Always double-check your substitution and algebraic steps to avoid simple calculation errors.

The perimeter of a rectangle is given by the formula: P = 2l + 2w. If the perimeter is 116 units and the length is 17 units, find the width of the rectangle.

Solve a geometry problem where you find the width of a rectangle given its length and perimeter. Understand how to apply the perimeter formula step-by-step, suitable for students in Grades 6-8.

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