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.