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:
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If \( W = 8 \) m: \[ \text{Length} = \frac{96}{8} = 12 \text{ m} \]
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If \( W = 12 \) m: \[ \text{Length} = \frac{96}{12} = 8 \text{ m} \]
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If \( W = 6 \) m: \[ \text{Length} = \frac{96}{6} = 16 \text{ m} \]
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If \( W = 4 \) m: \[ \text{Length} = \frac{96}{4} = 24 \text{ m} \]
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If \( W = 3 \) m: \[ \text{Length} = \frac{96}{3} = 32 \text{ m} \]
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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.