Question

The area of a rectangle is calculated with the formula a. equals LW if the area is of a rectangle is 52.5 M 2 and the width is 5M What is the length? Explain the solution to the real world problem.

Answer 1

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:

1. **Substitute the known values into the formula:**

\[
52.5 = L \times 5
\]

2. **To solve for \( L \), divide both sides of the equation by 5:**

\[
L = \frac{52.5}{5}
\]

3. **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.