To reduce the dimensions of the poster using a scale factor of \(\frac{1}{16}\), we can find the dimensions of the study card by multiplying the original dimensions by the scale factor.
Original Dimensions:
- Length of the poster = 36 inches
- Width of the poster = 24 inches
Using the Scale Factor of \(\frac{1}{16}\):
-
Length of the new study card: \[ \text{New Length} = 36 \text{ inches} \times \frac{1}{16} = \frac{36}{16} = 2.25 \text{ inches} \]
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Width of the new study card: \[ \text{New Width} = 24 \text{ inches} \times \frac{1}{16} = \frac{24}{16} = 1.5 \text{ inches} \]
Area of the New Study Card:
To find the area, we multiply the length by the width: \[ \text{Area} = \text{New Length} \times \text{New Width} = 2.25 \text{ inches} \times 1.5 \text{ inches} = 3.375 \text{ square inches} \]
Summary:
- Length of the new study card = 2.25 inches
- Width of the new study card = 1.5 inches
- Area of the new study card = 3.375 square inches