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!