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!