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The area of a rectangle is calculated with the formula A = lw. If the area of a rectangle is 52.5 m squared and the width is 5 m, what is the length? Explain the solution to the real-world problem.

A. The length is 10.5 m.
B. The length is 262.5 m.
C. The length is 262.5 m squared.
D. l = 10.5

3 answers

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

\[ A = lw \]

where:

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

We are given:

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

We need to solve for the length \( l \). Rearranging the formula to solve for \( l \), we get:

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

Now we can plug in the values:

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

Calculating this gives:

\[ l = 10.5 , \text{m} \]

Therefore, the length of the rectangle is 10.5 meters.

Now we can identify the answer choice that corresponds to our calculation:

A. The length is 10.5 m.

This is indeed correct.

To summarize the solution: We used the area formula for rectangles and rearranged it to find the unknown length. By substituting the known values (area and width), we calculated the length to be 10.5 meters in a straightforward manner.

are you positive this is correct

Yes, I am confident that the solution provided is correct. To summarize the steps clearly:

  1. The formula for the area of a rectangle is given by \( A = lw \), where \( A \) is the area, \( l \) is the length, and \( w \) is the width.

  2. In this problem, we know:

    • Area \( A = 52.5 , \text{m}^2 \)
    • Width \( w = 5 , \text{m} \)

  3. We need to find the length \( l \). Rearranging the area formula to solve for \( l \) gives: \[ l = \frac{A}{w} \]

  4. Substituting the known values into the formula: \[ l = \frac{52.5 , \text{m}^2}{5 , \text{m}} = 10.5 , \text{m} \]

Thus, the correct answer is A. The length is 10.5 m.

If you have any further questions or need clarification, feel free to ask!