To solve for the length of the rectangle given the area and the width, we can use the formula for the area of a rectangle:
\[ A = L \times W \]
Where:
- \( A \) is the area,
- \( L \) is the length, and
- \( W \) is the width.
In this scenario:
- The area \( A \) is 52.5 m²,
- The width \( W \) is 5 m.
We need to find the length \( L \).
Step-by-Step Solution:
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Substitute the known values into the formula:
\[ 52.5 = L \times 5 \]
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To solve for \( L \), divide both sides of the equation by 5:
\[ L = \frac{52.5}{5} \]
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Calculate the right side:
\[ L = 10.5 \]
So the length \( L \) of the rectangle is 10.5 meters.
Explanation of the Real-World Problem:
In this problem, we are working with a rectangle that has a fixed area. The area of a shape, in many real-world applications, can represent physical space or material, such as the size of a garden plot, the floor area of a room, or land that needs to be measured for various purposes.
Given that the area is known to be 52.5 m² and the width is fixed at 5 m, we were able to compute the length as 10.5 m.
This information might be useful for:
- Planning physical spaces (e.g., determining how much flooring material is needed),
- Agricultural applications (e.g., understanding how much land will be available for planting),
- Construction projects (e.g., laying out dimensions for a build).
Thus, the solution demonstrates a practical application of geometry in real-world contexts, where knowing the relationships between area, length, and width can be crucial for effective planning and resource management.
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