https://file.aiquickdraw.com/mathbot/file/1730070442759mgux8qto.jpg

Let's analyze the problem:

### Part 1: If the new length is 15
The width is given as 4 feet less than the length. So:

\[
\text{Width} = 15 - 4 = 11 \text{ feet}
\]

The perimeter formula is given by:

\[
y = 4x - 8
\]

Plugging \( x = 15 \):

\[
y = 4(15) - 8 = 60 - 8 = 52 \text{ feet}
\]

So, the width is **11 feet** and the perimeter is **52 feet**.

### Part 2: If the new perimeter is 59
We have the equation:

\[
y = 4x - 8
\]

Set \( y = 59 \):

\[
59 = 4x - 8
\]

Adding 8 to both sides:

\[
67 = 4x
\]

Dividing both sides by 4:

\[
x = 16.75 \text{ feet (length)}
\]

The width is:

\[
\text{Width} = x - 4 = 16.75 - 4 = 12.75 \text{ feet}
\]

### Final Answer:
- For length 15, the width is **11 feet** and the perimeter is **52 feet**.
- For a perimeter of 59, the length is **16.75 feet** and the width is **12.75 feet**.

Would you like more details or have any other questions? Here are some related questions:

1. How do you find the perimeter of a rectangle using its dimensions?
2. What is the relationship between the width and length in this problem?
3. How would the problem change if the width were given as 5 feet less than the length?
4. How can you verify the calculations for the perimeter equation?
5. What is the significance of solving linear equations in this context?

**Tip:** When finding dimensions given a condition like "4 feet less," always express the relationship algebraically to avoid mistakes!

You have a vegetable garden that you want to increase the size of to be able to plant more vegetables. You increased the length to x feet and the width will be 4 feet less than the length. The equation y = 4x - 8 represents the new perimeter, y, in feet, for a length of x feet. If the new length is 15, what is the new width and the new perimeter of the garden? If the new perimeter is 59, what is the new length and width of the garden?

Learn how to calculate the width and perimeter of a vegetable garden using linear equations. This problem covers key algebraic concepts with a formula for perimeter and relationships between length and width, ideal for students in Grades 7-9.

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