a gardener has 55 feet of fencing to be used to enclose a rectangular garden that had a border 2 feet wide surrounding it. If the length and width of the garden are to be the same what would be the dimensions of the garden

To solve this problem, we need to calculate the dimensions of the **inner garden** (the area within the fence, excluding the 2-foot border), given the constraint that the length and width are equal, and the total perimeter of the fencing is 55 feet.

### Step-by-Step Solution:

1. Let the side length of the **garden** be denoted by \( x \) (since the length and width are the same).

2. The **border** surrounding the garden is 2 feet wide, meaning the total dimensions including the border will be \( x + 2 + 2 = x + 4 \) feet for both the length and width (since the border adds 2 feet on each side).

3. The **perimeter of the entire enclosed area** (garden + border) is given by:
   \[
   P = 2 \times (x + 4) + 2 \times (x + 4) = 2(2(x + 4)) = 4(x + 4)
   \]

4. The gardener has **55 feet of fencing**, so we set up the equation for the perimeter:
   \[
   4(x + 4) = 55
   \]

5. Solve for \( x \):
   \[
   x + 4 = \frac{55}{4} = 13.75
   \]
   \[
   x = 13.75 - 4 = 9.75
   \]

Thus, the side length of the **garden** is **9.75 feet**.

### Final Answer:
The dimensions of the garden are **9.75 feet by 9.75 feet**.

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Would you like further details or clarification on any step?  
Here are some related questions you may find useful:

1. How do you calculate the area of the garden?
2. What would happen if the border width changes?
3. How would the problem change if the length and width were not the same?
4. What is the total area enclosed by the fence, including the garden and the border?
5. How does this solution apply to non-rectangular garden shapes?

**Tip**: Always ensure you account for any additional borders or margins when calculating dimensions from total measurements!

A gardener has 55 feet of fencing to be used to enclose a rectangular garden that had a border 2 feet wide surrounding it. If the length and width of the garden are to be the same, what would be the dimensions of the garden?

Learn how to calculate the dimensions of a rectangular garden with a 55-foot perimeter and a 2-foot border. The problem involves using geometric concepts and perimeter formulas, suitable for students in Grades 6-8.

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