The problem states:

"A rectangular garden has a length that is 4 meters greater than its width. The perimeter of the garden is 36 meters. Determine the dimensions of the garden."

Solution:

1. Let the width of the garden be $w$ meters.
2. The length of the garden will then be $w + 4$ meters.
3. The formula for the perimeter of a rectangle is: $\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$ Substituting the given perimeter and dimensions: $36 = 2 \times (w + w + 4)$
4. Simplify the equation: $36 = 2 \times (2w + 4)$ $36 = 4w + 8$
5. Subtract 8 from both sides: $28 = 4w$
6. Divide by 4: $w = 7$

Thus, the width of the garden is 7 meters, and the length is: $w + 4 = 7 + 4 = 11 \, \text{meters}.$

Final Answer:

• Width: 7 meters
• Length: 11 meters

Would you like a detailed explanation of any step?

Here are 5 related questions for practice:

1. What will the area of this rectangular garden be?
2. How would the dimensions change if the perimeter were doubled?
3. If the garden’s length were 6 meters more than its width, what would the dimensions be?
4. What is the relationship between perimeter and area for a rectangle?
5. How can this problem be solved graphically?

Tip: Always check your solution by substituting back into the original problem to ensure correctness.