An urban food co-op has been offered an abandoned plot of land for use as a community garden. The space for the garden measures 131 ft by 43 ft . City regulations specify that an easement of uniform width, x , must surround the garden. If the perimeter of the rectangular lot is 420 ft, what is the width of the easement?

To solve for the width of the easement, \( x \), we start by setting up the equation for the perimeter of the entire rectangular lot, including the easement.

### Step 1: Express the dimensions of the lot including the easement.
- The original dimensions of the garden are 131 ft by 43 ft.
- The easement adds a uniform width \( x \) around the entire garden, so the dimensions of the lot including the easement become:
  - Length: \( 131 + 2x \) ft
  - Width: \( 43 + 2x \) ft

### Step 2: Set up the equation for the perimeter.
The perimeter \( P \) of a rectangle is given by:
\[
P = 2(\text{Length} + \text{Width})
\]
Substituting the dimensions of the lot including the easement:
\[
420 = 2\left((131 + 2x) + (43 + 2x)\right)
\]

### Step 3: Simplify and solve for \( x \).
\[
420 = 2\left(131 + 43 + 4x\right)
\]
\[
420 = 2\left(174 + 4x\right)
\]
\[
420 = 348 + 8x
\]
\[
420 - 348 = 8x
\]
\[
72 = 8x
\]
\[
x = \frac{72}{8} = 9 \text{ ft}
\]

### Conclusion:
The width of the easement is \( \boxed{9} \) feet.

Would you like further details or have any questions? Here are some related questions:

1. What is the area of the garden without the easement?
2. How much area does the easement take up?
3. What is the total area of the entire lot including the easement?
4. How would the easement width change if the perimeter was different?
5. What happens if the easement needs to be a certain percentage of the garden's width?

**Tip:** Remember, when solving perimeter problems involving added dimensions, always account for the uniform addition on all sides by multiplying the added width by 2.

Learn how to calculate the width of an easement required around a community garden using the perimeter formula for rectangles. This problem involves solving a linear equation to determine the uniform width of the easement. Suitable for students in Grades 7-9.

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