To find the new scale that corresponds to Raphael's desired patio size of 15 feet on each side, let's first recap the original scale you've provided:
- Original scale: \(1 \text{ inch} = 4 \text{ feet}\)
Now, let's analyze the situation where Raphael builds a patio that is \(15 \text{ feet}\) on each side.
Step 1: Determine the new scale.
We want to find the equivalent representation in inches for \(15 \text{ feet}\).
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Starting from the original scale: \[ \text{Original scale: } 1 \text{ inch} = 4 \text{ feet} \]
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To find the number of inches that represents \(15 \text{ feet}\): \[ \text{length in inches} = \frac{\text{length in feet}}{\text{feet per inch}} = \frac{15 \text{ feet}}{4 \text{ feet per inch}} = 3.75 \text{ inches} \]
Step 2: Determine the new scale.
Since \(1 \text{ inch}\) originally represented \(4 \text{ feet}\), now we have:
- \(15 \text{ feet}\) corresponds to \(3.75 \text{ inches}\).
To find the new scale where \(1 \text{ inch}\) represents how many feet: \[ \text{New scale factor} = \frac{15 \text{ feet}}{3.75 \text{ inches}} = 4 \text{ feet per inch} \]
Conclusion:
The change of scale does not alter the proportionality since both scales end up implying \(1 \text{ inch} = 4 \text{ feet}\).
Thus:
- The change of scale means that \(1 \text{ inch}\) still represents \(4\) feet. The new scale remains \(1 \text{ inch} = 4 \text{ feet}\).
In summary, the new scale remains the same at \(4\) feet per inch, meaning that the statement in your question essentially retains the same measurement despite the differing sizes of the squares.