To determine the scale factor Leo used for the enlargement of the photograph, we first need to know the original and enlarged side lengths of the jewelry.
Original side length:
- Each side of the original pentagon measures 3 centimeters.
Enlarged side length:
- We need the enlarged side length to evaluate the potential scale factors given.
If we assume the scale factors provided are directly related to the enlarged side lengths, we can compute hypothetical enlarged lengths corresponding to each option:
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Scale factor of 11: \[ 3 \times 11 = 33 \text{ cm} \]
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Scale factor of \( \frac{3}{8} \): \[ 3 \times \frac{3}{8} = \frac{9}{8} = 1.125 \text{ cm} \]
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Scale factor of \( 2 \frac{1}{3} \) (which equals \( \frac{7}{3} \)): \[ 3 \times \frac{7}{3} = 7 \text{ cm} \]
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Scale factor of \( 2 \frac{2}{3} \) (which equals \( \frac{8}{3} \)): \[ 3 \times \frac{8}{3} = 8 \text{ cm} \]
Summary of enlarged lengths:
- Scale factor of 11: 33 cm
- Scale factor of \( \frac{3}{8} \): 1.125 cm
- Scale factor of \( 2 \frac{1}{3} \): 7 cm
- Scale factor of \( 2 \frac{2}{3} \): 8 cm
Since the problem does not specify the value of the enlarged side length, we have to consider the most reasonable option typically used for enlargements in design contexts.
You may already have the actual enlarged side length to select the correct factor among those provided. If the larger size is not known, you cannot definitively determine the scale factor based on the options given.
If we are looking for a reasonable enlargement, the scale factor of 2 2/3 (which equals 8 cm) seems likely, because it leads to a whole number that represents a substantial size increase.
If you provide the actual measurement of the enlarged side length, we can conclude with certainty which scale factor was used. Otherwise, the likely answer based on common practice in jewelry design would be 2 2/3.