To determine the dimensions and area of the study card after reducing the poster using a scale factor of \( \frac{1}{6} \), we can follow these steps:
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Calculate the Length of the New Study Card: \[ \text{Length of the new study card} = \text{Original Length} \times \text{Scale Factor} = 36 , \text{inches} \times \frac{1}{6} = 6 , \text{inches} \]
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Calculate the Width of the New Study Card: \[ \text{Width of the new study card} = \text{Original Width} \times \text{Scale Factor} = 24 , \text{inches} \times \frac{1}{6} = 4 , \text{inches} \]
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Calculate the Area of the New Study Card: \[ \text{Area of the new study card} = \text{Length} \times \text{Width} = 6 , \text{inches} \times 4 , \text{inches} = 24 , \text{square inches} \]
Now, we summarize the results:
- Length of the new study card = 6 inches
- Width of the new study card = 4 inches
- Area of the new study card = 24 square inches