Question

An expression for the length of the rectangle in terms of the width would be Response area

The formula for the area of a rectangle is Response area

Using trial and error, if the area is 96 m^2, then the length and width are Response area

Answer 1

To express the length of a rectangle in terms of its width, we can use the formula for the area of a rectangle:

### Formula for the area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]

If we denote the width as \( w \) and the length as \( l \), we can rearrange this formula to express the length in terms of the width:

\[
l = \frac{\text{Area}}{w}
\]

### Given that the area is 96 m²:
Thus,

\[
l = \frac{96}{w}
\]

### Using trial and error:
To find possible dimensions for the rectangle (length and width) that yield an area of 96 m², we can pick various values for the width \( w \) and calculate the corresponding length \( l \):

1. If \( w = 8 \, \text{m} \):
\[
l = \frac{96}{8} = 12 \, \text{m}
\]

2. If \( w = 6 \, \text{m} \):
\[
l = \frac{96}{6} = 16 \, \text{m}
\]

3. If \( w = 4 \, \text{m} \):
\[
l = \frac{96}{4} = 24 \, \text{m}
\]

4. If \( w = 12 \, \text{m} \):
\[
l = \frac{96}{12} = 8 \, \text{m}
\]

### Summary of Dimensions:
You will find that pairs of width (\( w \)) and length (\( l \)) that produce an area of 96 m² are:
- Width = 8 m, Length = 12 m
- Width = 6 m, Length = 16 m
- Width = 4 m, Length = 24 m
- Width = 12 m, Length = 8 m

You can continue this process with other values as needed, ensuring the product of width and length always equals 96 m².