Question

The area of a rectangle is calculated with the formula \(A=lw\). If the area of a rectangle is \(52.5\ \text{m}^2\) and the width is 5 m, what is the length? Explain the solution to the real-world problem.

Answer 1

To find the length of the rectangle given its area and width, we use the formula for the area of a rectangle:

\[
A = l \times w
\]

where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We know from the problem that:

- \(A = 52.5\ \text{m}^2\)
- \(w = 5\ \text{m}\)

We need to solve for the length \(l\).

To do this, we can rearrange the area formula to solve for \(l\):

\[
l = \frac{A}{w}
\]

Now, we can substitute in the values we have:

\[
l = \frac{52.5\ \text{m}^2}{5\ \text{m}}
\]

Calculating this gives:

\[
l = \frac{52.5}{5} = 10.5\ \text{m}
\]

Thus, the length of the rectangle is \(10.5\ \text{m}\).

### Explanation of the Solution to the Real-World Problem:

In a real-world scenario, you might be dealing with space requirements for a certain area, such as the floor space in a room or the base of a garden plot. The problem gives us the total area of the rectangle (52.5 square meters) that we need for a specific purpose (like laying down flooring or planting). The width of this area is already known to be 5 meters, perhaps due to existing constraints (like walls or pathways).

Using the area formula, we calculated that to achieve the desired area with that specific width, we would need a length of 10.5 meters. This length meets the requirement for the specified area, allowing for proper use and planning of the space at hand.