To solve the problem, we start with the formula for the area of a rectangle:
\[ A = lw \]
Where:
- \( A \) is the area,
- \( l \) is the length,
- \( w \) is the width.
We know from the problem that:
- \( A = 52.5 , \text{m}^2 \)
- \( w = 5 , \text{m} \)
We need to find the length \( l \). We can rearrange the formula to solve for length:
\[ l = \frac{A}{w} \]
Now we can plug in the values we have:
\[ l = \frac{52.5 , \text{m}^2}{5 , \text{m}} \]
Calculating this gives:
\[ l = 10.5 , \text{m} \]
Thus, the length of the rectangle is 10.5 meters.
Explanation of the solution:
We started with the given area of the rectangle and the width. By using the area formula and rearranging it, we were able to express the length in terms of the area and the width. After substituting the known values into the equation, we performed the division to find the length. The correct response is that the length is \( 10.5 , \text{m} \).
The incorrect options included values that were not calculated accurately based on the area and width given. Specifically, the values \( 262.5 , \text{m} \) and \( 262.5 , \text{m}^2 \) do not appropriately apply to the calculations relevant to the dimensions of the rectangle based on the provided area.
Thus, the length is confirmed to be \( 10.5 , \text{m} \).
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