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)

Answer 1

To find the length of the rectangle when the area and width are known, we can use the formula for the area of a rectangle, which is given by:

\[ A = l \times w \]

Where:

• \( A \) = area of the rectangle
• \( l \) = length of the rectangle
• \( w \) = width of the rectangle

Given that the area \( A = 52.5 \) m² and the width \( w = 5 \) m, we can substitute these values into the formula and solve for the length \( l \).

Starting with the formula:

\[ 52.5 = l \times 5 \]

To solve for \( l \), divide both sides of the equation by \( 5 \):

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

Calculating this gives:

\[ l = 10.5 , \text{m} \]

Explanation of the Solution:

In this real-world problem, we have a rectangle with a known area of \( 52.5 \) square meters and a specified width of \( 5 \) meters. We need to find out how long the rectangle is. By using the formula for the area, we rearranged the equation to isolate the length. After performing the division, we find that the length of the rectangle is \( 10.5 \) meters.

This problem illustrates a common scenario in geometry where one dimension of a shape is known, and you need to find another dimension based on a fixed area. The solution shows the process of using basic algebraic manipulation to solve for the unknown variable.