To find the scale factor between the original size of the patio and the size that Raphael wants to build, we first need to convert the lengths from feet to inches using the scale provided:
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Original square patio size:
- Side length: 12 feet
- Since 1 inch = 4 feet, we convert: \[ 12 \text{ feet} = \frac{12 \text{ feet}}{4 \text{ feet/inch}} = 3 \text{ inches} \]
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New square patio size:
- Side length: 15 feet
- Similarly, convert: \[ 15 \text{ feet} = \frac{15 \text{ feet}}{4 \text{ feet/inch}} = 3.75 \text{ inches} \]
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Calculating the scale factor:
- To find the change in the scale factor, we divide the side length of the new patio by the side length of the original patio: \[ \text{Scale factor} = \frac{\text{New side length}}{\text{Original side length}} = \frac{3.75 \text{ inches}}{3 \text{ inches}} = 1.25 \]
Thus, the change in the scale factor is 1.25.