To reduce the dimensions of the original poster using a scale factor of \( \frac{1}{6} \), we can apply the scale factor to both the length and the width of the poster.
Step 1: Calculate the dimensions of the study card
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Length of the new study card: \[ \text{Length} = \text{Original Length} \times \text{Scale Factor} \] \[ \text{Length} = 36 \text{ inches} \times \frac{1}{6} = 6 \text{ inches} \]
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Width of the new study card: \[ \text{Width} = \text{Original Width} \times \text{Scale Factor} \] \[ \text{Width} = 24 \text{ inches} \times \frac{1}{6} = 4 \text{ inches} \]
Step 2: Calculate the area of the study card
The area of a rectangle is calculated as: \[ \text{Area} = \text{Length} \times \text{Width} \] \[ \text{Area} = 6 \text{ inches} \times 4 \text{ inches} = 24 \text{ square inches} \]
Final 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
These are the dimensions and area of the study card.