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The image you provided contains a word problem related to fencing a rectangular garden. Here’s a transcription of the problem from the image:

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**Problem:**

The area of a 100 feet wide rectangular piece of land is 5000 square feet. You want to make a garden along one of the shorter lengths of this area. There is a 1-foot wide path around the garden. You want to fence the garden using 100 feet of fencing material. Find the length of the garden. (Note: Include the cost of the fence and its installation.)

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**Steps to solve the problem:**

1. **Identify the given information:**
   - The total area of the land is 5000 square feet.
   - The width of the land is 100 feet.
   - There is a 1-foot wide path around the garden.
   - You have 100 feet of fencing material to fence the garden.

2. **Calculate the dimensions of the garden:**
   - First, find the length of the land using the area formula \( \text{Area} = \text{length} \times \text{width} \):
     \[
     \text{Length} = \frac{\text{Area}}{\text{Width}} = \frac{5000 \, \text{sq ft}}{100 \, \text{ft}} = 50 \, \text{feet}
     \]
   - Therefore, the dimensions of the land are 100 feet by 50 feet.

3. **Consider the 1-foot wide path:**
   - The garden will be inside this 1-foot wide path.
   - The garden's dimensions will be reduced by 1 foot on all sides due to the path.
   - So, the dimensions of the garden will be:
     \[
     \text{Length of the garden} = 50 - 2 \times 1 = 48 \, \text{feet}
     \]
     \[
     \text{Width of the garden} = 100 - 2 \times 1 = 98 \, \text{feet}
     \]

4. **Fencing requirement:**
   - The perimeter of the garden (where the fence is needed) is given by the formula:
     \[
     \text{Perimeter} = 2 \times (\text{Length} + \text{Width})
     \]
     \[
     \text{Perimeter} = 2 \times (48 + 98) = 2 \times 146 = 292 \, \text{feet}
     \]
   - However, you only have 100 feet of fencing material.

5. **Determine the appropriate garden dimensions:**
   - To find the actual length of the garden that can be fenced with the available material, you need to adjust either the width or the length.
   - Set up an equation for the perimeter to match the available fencing material:
     \[
     2 \times (L + W) = 100 \, \text{feet}
     \]
   - Let \( L \) and \( W \) be the adjusted length and width of the garden (after accounting for the path):
     \[
     2 \times (L + W) = 100
     \]
     \[
     L + W = 50
     \]

     Given the reduced dimensions due to the path:
     \[
     L = 48 \, \text{feet (Length after path deduction)}
     \]
     \[
     W = \text{To be determined based on the condition above.}
     \]

   - You then need to calculate \( W \) and ensure it fits the given material constraint.

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Let me know if you need further details or clarifications on the next steps for finding the exact dimensions of the garden!

The area of a rectangular garden is given, and there is a path around it. You need to find the length of the garden using the given fencing material.

This problem involves determining the length of a rectangular garden that includes a 1-foot wide path and has specific fencing constraints. Suitable for students in Grades 7-9, this problem covers essential geometric concepts and algebraic problem-solving.

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