To find the length of the rectangle when the area and width 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.
In this case, we are given:
- The area \( A = 52.5 , \text{m}^2 \)
- The width \( w = 5 , \text{m} \)
We want to find the length \( l \). To do this, we can rearrange the formula to solve for \( l \):
\[ l = \frac{A}{w} \]
Now, we can substitute the values we have:
\[ l = \frac{52.5 , \text{m}^2}{5 , \text{m}} \]
\[ l = 10.5 , \text{m} \]
Thus, the length of the rectangle is \( 10.5 , \text{m} \).
Explanation of the Solution
This approach allows us to determine the necessary dimension (length) of a rectangle when we know the total area and one of the dimensions (width). In real-world scenarios, such as planning a garden, constructing a room, or laying down flooring, it is common to need to find one dimension when the other dimension and total area are provided. By using simple algebraic manipulation of the area formula, we can find the unknown dimension easily. In this case, knowing that the area is \( 52.5 , \text{m}^2 \) and the width is \( 5 , \text{m} \) directly leads us to conclude that a length of \( 10.5 , \text{m} \) will yield the correct area for the rectangle in question.