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.

Question

A). \(l=10.5\)

B). The length is 10.5 m.

C). The length is 262.5 m.

D). The length is \(262.5\ \text{m}^2\).

Answer 1

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

\[ A = l \cdot w \]

where:

• \(A\) is the area,
• \(l\) is the length,
• \(w\) is the width.

Given:

• The area \(A = 52.5\ \text{m}^2\),
• The width \(w = 5\ \text{m}\).

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

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

Now substituting the known values:

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

Calculating this:

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

Therefore, the length of the rectangle is \(10.5\) m.

Now, considering the options provided:

A). \(l=10.5\) - This is true but not complete as an answer.

B). The length is 10.5 m. - This is a complete and correct statement.

C). The length is 262.5 m. - This is incorrect.

D). The length is \(262.5\ \text{m}^2\). - This is incorrect because length should be measured in meters, not square meters.

The best answer is:

B). The length is 10.5 m.