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

Answer 1

To derive an expression for the length of a rectangle in terms of the width, we start with the formula for the area of a rectangle:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Given that the area is 96 m², we can write:

\[
96 = \text{Length} \times \text{Width}
\]

To express the length in terms of the width (let's denote the width as \( W \)), we can rearrange this formula:

\[
\text{Length} = \frac{96}{W}
\]

Now, using trial and error to find possible pairs of length and width that yield an area of 96 m², we can try different widths:

1. **If \( W = 8 \) m:**
\[
\text{Length} = \frac{96}{8} = 12 \text{ m}
\]

2. **If \( W = 12 \) m:**
\[
\text{Length} = \frac{96}{12} = 8 \text{ m}
\]

3. **If \( W = 6 \) m:**
\[
\text{Length} = \frac{96}{6} = 16 \text{ m}
\]

4. **If \( W = 4 \) m:**
\[
\text{Length} = \frac{96}{4} = 24 \text{ m}
\]

5. **If \( W = 3 \) m:**
\[
\text{Length} = \frac{96}{3} = 32 \text{ m}
\]

6. **If \( W = 2 \) m:**
\[
\text{Length} = \frac{96}{2} = 48 \text{ m}
\]

From these calculations, we find the following pairs of length and width that yield an area of 96 m²:

- Width = 8 m, Length = 12 m
- Width = 12 m, Length = 8 m
- Width = 6 m, Length = 16 m
- Width = 4 m, Length = 24 m
- Width = 3 m, Length = 32 m
- Width = 2 m, Length = 48 m

These are all the combinations of length and width for the rectangle with an area of 96 m².