The area of a rectangle is calculated with the formula A=lw . If the area of a rectangle is 52.5 m^(2) and the width is 5 m, what is the length? Explain the solution to the real-world problem.

Answer 1

To find the length of a rectangle when the area and the width are given, you can use the formula for the area of the rectangle:

\[ A = l \times w \]

where:

• \( A \) is the area,
• \( l \) is the length, and
• \( w \) is the width.

In this case, you are given:

• \( A = 52.5 \) m² (the area of the rectangle),
• \( w = 5 \) m (the width of the rectangle).

You need to find the length \( l \). You can rearrange the formula to solve for \( l \):

\[ l = \frac{A}{w} \]

Now you can substitute the values of \( A \) and \( w \) into the formula:

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

Next, perform the division:

\[ l = 10.5 \]

So, the length of the rectangle is \( 10.5 \) m.

Explanation of the Solution:

In this real-world problem, you might be dealing with a physical rectangle, such as a garden plot or a room. The area of 52.5 m² indicates how much space the rectangle covers, while the width of 5 m tells us how wide the rectangle is. By using the formula for the area of a rectangle, we were able to determine that the length of the rectangle must be 10.5 m.

This information can be useful for various applications, such as planning how much material is needed for a fence around the rectangle, planting specific rows of plants in a garden, or determining how to arrange furniture in a room based on the specified area and width. Understanding dimensions in this way helps in making informed decisions about space and resources.

Answer 2

The length is 262.5 m^2

The length is 262.5 m.

The length is 10.5 m.

l=10.5

Answer 3

It looks like you are summarizing the calculations and results. Let’s clarify these points to ensure all information is accurate:

1. Rectangle Area Calculation: The area of a rectangle is given by the formula \( A = l \times w \).

2. Given Values:

   • Width \( w = 5 \) m
   • Area \( A = 52.5 \) m²

3. Finding the Length: To find the length \( l \), we rearranged the formula: \[ l = \frac{A}{w} = \frac{52.5}{5} \]

4. Calculation: \[ l = 10.5 \text{ m} \]

Therefore:

• The length \( l \) of the rectangle is 10.5 m.

Explanation of Your Summary:

• Length is 262.5 m²: This seems to be a mix-up, as area is measured in square units (m²), and it should reflect the product of length and width. The area based on the calculation we did is 52.5 m², not 262.5 m².

• Length is 262.5 m: This also appears to be incorrect based on our calculations. The length we calculated is 10.5 m, which is the correct dimension based on the given width and area.

• Length is 10.5 m: This is correct and confirms our earlier calculation.

In summary, the correct length of the rectangle is 10.5 m based on the provided area and width. Please let me know if you need clarification or further assistance!