Question

The area of a rectangle is calculated with the formula A=lw . If the area of a rectangle is 52.5 m2 and the width is 5 m, what is the length? Explain the solution to the real-world problem.(1 point) Responses The length is 262.5 m. The length is 262.5 m. The length is 10.5 m. The length is 10.5 m. The length is 262.5 m2. The length is 262.5 m squared . l=10.5

Answer 1

To find the length of a rectangle when the area \( A \) and width \( w \) are known, we can use the formula for the area of a rectangle:

\[
A = l \times w
\]

Where:

- \( A \) is the area
- \( l \) is the length
- \( w \) is the width

We are given:

- Area \( A = 52.5 \, m^2 \)
- Width \( w = 5 \, m \)

We need to solve for the length \( l \). We can rearrange the formula to solve for \( l \):

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

Substituting the values into the equation:

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

Now we perform the division:

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

Thus, the length \( l \) is 10.5 m.

### Explanation of the Solution:

In this real-world problem, we are calculating the length of a rectangle based on its given area and width. The formula \( A = lw \) allows us to determine how these dimensions relate to each other. Given that we know one dimension (the width), and we have the total area, we can easily compute the other dimension (the length) by rearranging the formula. The significant part is understanding that the dimensions must have consistent units, which in this case are both in meters (m).

The correct answer is therefore **the length is 10.5 m**.