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 \( l \):
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If \( w = 8 , \text{m} \): \[ l = \frac{96}{8} = 12 , \text{m} \]
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If \( w = 6 , \text{m} \): \[ l = \frac{96}{6} = 16 , \text{m} \]
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If \( w = 4 , \text{m} \): \[ l = \frac{96}{4} = 24 , \text{m} \]
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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.
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