To find the length of the rectangle given the area and width, we can use the formula for the area of a rectangle, which is:
\[ A = l \times w \]
Where:
- \( A \) is the area,
- \( l \) is the length,
- \( w \) is the width.
Given:
- Area (\( A \)) = 52.5 m²,
- Width (\( w \)) = 5 m.
We need to find the length (\( l \)). We can rearrange the area formula to solve for \( l \):
\[ l = \frac{A}{w} \]
Now, we can substitute the known values into the equation:
\[ l = \frac{52.5 , \text{m}^2}{5 , \text{m}} \]
Calculating this:
\[ l = 10.5 , \text{m} \]
So, the length of the rectangle is 10.5 m.
Explanation of the Real-World Problem:
In a real-world context, knowing that the area of a rectangular plot is 52.5 m² and the width is 5 m helps us determine how long the plot is. Once calculated, we find that the length is 10.5 m. This information might be useful for someone looking to determine whether they can fit certain structures or plants along this plot of land, or for planning purposes related to construction or landscaping. Thus, understanding the relationships between area, length, and width is essential for effectively utilizing space in various applications.