To find a missing measurement of an original rectangle using the dimensions of a reduced rectangle and one given measurement of the original rectangle, follow these steps:
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Understand the Relationship: The reduced rectangle is often a scaled-down version of the original rectangle. The dimensions of the reduced rectangle are typically a certain percentage or fraction of the dimensions of the original rectangle.
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Identify the Given Measurement: Start with the measurement you have for the original rectangle. This could be either the length or the width.
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Use the Scaling Factor: Determine the scaling factor between the original rectangle and the reduced rectangle. For example, if each dimension of the reduced rectangle is half of the corresponding dimension of the original rectangle, the scaling factor is 0.5.
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Calculate the Missing Dimension:
- If you know the length of the original rectangle and the corresponding length of the reduced rectangle, you can find the missing width of the original rectangle using the ratio.
- For example, if the original rectangle's length is given as \( L \) and the reduced rectangle's length is \( l_r \), then: \[ \text{Scaling Factor} = \frac{l_r}{L} \]
- If you also know the width of the reduced rectangle \( w_r \), you can find the width of the original rectangle \( W \) using: \[ W = \frac{w_r}{\text{Scaling Factor}} \]
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Example:
- Let's assume the original rectangle has a length of 10 units, and the reduced rectangle has a length of 5 units and a width of 2.5 units.
- The scaling factor for length is: \[ \text{Scaling Factor} = \frac{5}{10} = 0.5 \]
- To find the original width \( W \): \[ W = \frac{2.5}{0.5} = 5 \text{ units} \]
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Conclusion: By knowing either the length or the width of the original rectangle and using the dimensions of the reduced rectangle along with the scaling factor, you can accurately find the missing measurement of the original rectangle.
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