To find the length of a rectangle when given the area and the width, we can rearrange the formula for the area of a rectangle, \( A = lw \), where:
- \( A \) = area
- \( l \) = length
- \( w \) = width
Given that the area \( A \) is 52.5 m² and the width \( w \) is 5 m, we can substitute these values into the formula:
\[ 52.5 = l \cdot 5 \]
Now, to find \( l \), we need to isolate it. We can do this by dividing both sides of the equation by 5:
\[ l = \frac{52.5}{5} \]
Calculating the right side:
\[ l = 10.5 \]
So the length of the rectangle is 10.5 m.
Real-World Problem Explanation:
Imagine you are planning to create a garden plot in your backyard that has a rectangular shape. You have determined that the total area of the garden you want is 52.5 square meters. You also decided that you want the width of the garden to be 5 meters. To find out how long your garden should be to achieve that area, you apply the area formula for a rectangle, which is \( A = lw \).
After substituting the known values into the formula, you carried out the calculation and found that the length should be 10.5 meters to ensure that the area of your garden meets your requirements.
Thus, option A (the length is 10.5m) is correct, while the other options either present incorrect units or values.