A rectangular city park is $\frac{6}{8}\text{ mi}$ long. The park has an area of $\frac{1}{4}\text{ mi}^2$. What is the width of the park? Show your work.

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05-11-2026
Mathematics

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A rectangular city park is $\frac{6}{8}\text{ mi}$ long. The park has an area of $\frac{1}{4}\text{ mi}^2$. What is the width of the park? Show your work.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T18:09:26-05:00

Identify the given values: length $L = \frac{6}{8} = \frac{3}{4}$ mi and area $A = \frac{1}{4}$ mi$^2$.
Use the area formula for a rectangle: $\text{Area} = \text{length} \times \text{width}$.
Solve for the width using the equation $W = \frac{A}{L} = \frac{1/4}{3/4}$.
Simplify the resulting fraction to find the width: $\boxed{\frac{1}{3} \text{ mi}}$.

Explanation

Identify the given values and the formula.

The problem asks for the width of a rectangular city park given its length and its area. We are given the following information:

The length of the rectangular park, $L = \frac{6}{8}$ mi.
The area of the rectangular park, $A = \frac{1}{4}$ mi$^2$.

We know that the formula for the area of a rectangle is:
\[\text{Area} = \text{length} \times \text{width}\]
We can represent this as:
\[A = L \times W\]
where $W$ is the width of the park. Our goal is to solve for $W$.

Set up the equation and solve for the width.

First, let's simplify the fraction for the length to make the division easier:
\[L = \frac{6}{8} = \frac{3}{4} \text{ mi}\]

Now, we can substitute the known values into the area formula:
\[\frac{1}{4} = \frac{3}{4} \times W\]
To solve for $W$, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by the length, $\frac{3}{4}$, or equivalently, by multiplying both sides by its reciprocal, which is $\frac{4}{3}$:
\[W = \frac{1}{4} \times \frac{4}{3}\]

Calculate and simplify the final result.

Now perform the multiplication:
\[W = \frac{1 \times 4}{4 \times 3} = \frac{4}{12}\]
Finally, simplify the fraction $\frac{4}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
\[W = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}\]

The width of the park is $\frac{1}{3}$ miles. The final answer is $\boxed{\frac{1}{3} \text{ mi}}$.

Examples

Understanding how to calculate the dimensions of a rectangle given its area is essential for many real-life applications. For instance, if you are planning to build a rectangular garden or a patio in your backyard and you know the total amount of space you have (area) and how long one side can be, you can easily determine how wide the other side needs to be to fit your space. Whether you are laying out pavers for a walkway or determining the necessary fencing for a plot of land, this simple algebraic relationship $W = \frac{A}{L}$ ensures your projects fit perfectly.