- Identify the relationship between area, length, and width: \(A = l \times w\).
- Substitute the given area (\(72 \text{ in.}^2\)) and width (\(8 \text{ in.}\)) into the equation.
- Solve the equation \(72 = l \times 8\) by dividing by 8.
- Conclude that the length of the rectangle is \(\boxed{9 \text{ in.}}\).
Explanation
- Define the problem and the area formula.
The objective is to find the length of a rectangle given its area and one side length (width).
Given data:
- Area of the rectangle \(A = 72 \text{ in.}^2\).
- Width of the rectangle \(w = 8 \text{ in.}\).
The area \(A\) of a rectangle is defined as the product of its length \(l\) and width \(w\):
\[A = l \times w\]
We are asked to find the length \(l\).
- Solve for the length.
Substitute the known values into the area formula:
\[72 \text{ in.}^2 = l \times 8 \text{ in.}\]
To isolate the length \(l\), divide both sides of the equation by the width \(w = 8 \text{ in.}\):
\[l = \frac{72 \text{ in.}^2}{8 \text{ in.}}\]
\[l = 9 \text{ in.}\]
Thus, the length of the rectangle is \(9 \text{ in.}\).
Examples
Imagine you are building a rectangular garden bed in your backyard. If you have enough soil to cover an area of \(72 \text{ square feet}\) and you have decided that one side of the garden bed must be \(8 \text{ feet}\) long to fit perfectly against your house wall, you can use this formula to determine the necessary length of the other side. Knowing the length is \(9 \text{ feet}\) allows you to correctly measure and mark out the garden space, ensuring you order exactly the right amount of materials.