The area of a rectangle is calculated with the formula A=lw . If the area of a rectangle is 52.5 m2 and the width is 5 m, what is the length? Explain the solution to the real-world problem.(1 point)

Question

Responses

The length is 262.5 m.
The length is 262.5 m.

The length is 10.5 m.
The length is 10.5 m.

l=10.5
l equals 10.5

The length is 262.5 m2.

Answer 1

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

\[ A = lw \]

Where:

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

Given:

• Area \( A = 52.5 , m^2 \)
• Width \( w = 5 , m \)

We need to find the length \( l \).

We can rearrange the formula to solve for \( l \):

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

Substituting the known values into the equation:

\[ l = \frac{52.5 , m^2}{5 , m} \]

Calculating:

\[ l = 10.5 , m \]

Thus, the length of the rectangle is 10.5 meters.

Real-World Problem Explanation

In a real-world context, this could represent a physical rectangular garden or room where you want to find out how long one side is, given the total area and the width. Knowing that the area is fixed at 52.5 m² and one dimension (the width) is known to be 5 m allows us to easily compute the required length to ensure the entire area is utilized efficiently, equipping us with the knowledge to plan out the space effectively. Therefore, the correct response is:

The length is 10.5 m.