In this problem, we're asked to find the length and width of a rectangular garden where the perimeter is 36 feet, and the length is 4 feet more than the width.

Step-by-Step Solution:

1. Use the perimeter formula for a rectangle: The perimeter $P$ of a rectangle is given by: $P = 2 \times (\text{Length} + \text{Width})$ Given that the perimeter is 36 feet: $36 = 2 \times (\text{Length} + \text{Width})$ Simplifying this: $\text{Length} + \text{Width} = 18 \quad \text{(Divide both sides by 2)}$

2. Express the length in terms of the width: We are told that the length is 4 feet more than the width. So, let the width be denoted as $w$ and the length as $w + 4$.

3. Set up an equation for the width: Substitute $w + 4$ for the length in the equation $\text{Length} + \text{Width} = 18$: $(w + 4) + w = 18$ Simplifying: $2w + 4 = 18$

4. Solve for the width: Subtract 4 from both sides: $2w = 14$ Divide both sides by 2: $w = 7$

5. Find the length: Since the length is 4 feet more than the width, the length is: $\text{Length} = 7 + 4 = 11$

Thus, the length of the rectangular garden is 11 feet, and the width is 7 feet.

Would you like more details or have any questions? Here are a few related questions:

1. How would you calculate the area of this rectangle?
2. How can you derive the perimeter of any rectangle?
3. What happens if the length and width are equal?
4. How would the perimeter change if the dimensions were doubled?
5. How can we solve similar problems using algebraic expressions?

Tip: When dealing with word problems involving rectangles, translating the given relationships into algebraic expressions can simplify the solution process.