https://file.aiquickdraw.com/mathbot/file/1730491005605lflqd2k0.jpg

To solve this problem, let's break down the information provided and set up equations:

1. **Define variables**:
   - Let \( w \) represent the width of the rectangle (in feet).
   - Let \( l \) represent the length of the rectangle (in feet).

2. **Set up relationships based on the problem**:
   - The length is stated to be \( 2 \frac{1}{2} \) times the width. Converting \( 2 \frac{1}{2} \) to an improper fraction gives us \( \frac{5}{2} \).
   - Thus, we can express the length as:
     \[
     l = \frac{5}{2}w
     \]

3. **Use the perimeter formula**:
   - The formula for the perimeter of a rectangle is:
     \[
     P = 2l + 2w
     \]
   - The problem states that the perimeter is 42 feet, so we set up the equation:
     \[
     2l + 2w = 42
     \]

4. **Substitute \( l = \frac{5}{2}w \) into the perimeter equation**:
   \[
   2\left(\frac{5}{2}w\right) + 2w = 42
   \]
   Simplify this equation:
   \[
   5w + 2w = 42
   \]
   \[
   7w = 42
   \]
   \[
   w = 6
   \]

5. **Find the length**:
   - Substitute \( w = 6 \) back into the equation for \( l \):
     \[
     l = \frac{5}{2} \cdot 6
     \]
     \[
     l = 15
     \]

6. **Conclusion**:
   - The dimensions of the rectangle are:
     - Width = 6 feet
     - Length = 15 feet

Would you like more details on any step or have further questions?

### Related Questions
1. How do you convert a mixed number into an improper fraction?
2. What is the formula for the area of a rectangle?
3. How would you set up an equation if the perimeter and area of a rectangle were both known?
4. How can you check if the dimensions satisfy the given perimeter condition?
5. What are the dimensions if the perimeter were different, say 50 feet?

### Tip
When working with mixed numbers in word problems, always convert them to improper fractions to simplify calculations.

The length of a rectangle is 2 1/2 times the width, and the perimeter is 42 feet. What are the dimensions of this rectangle?

Learn how to find the dimensions of a rectangle given that its length is 2 1/2 times the width and the perimeter is 42 feet. This problem covers algebraic techniques and geometric concepts, ideal for students in Grades 6-8.

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