Question

Original scale: 1 inch = 4 feet. A square with 12 foot sides and a larger square with 15 foot sides.
Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side.

The change in the scale factor is
5/4
.
The change of scale means that 1 inch represented 4 feet, but now 1 inch represents
feet.

Answer 1

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 \(15 \text{ feet}\).

1. Starting from the original scale:
\[
\text{Original scale: } 1 \text{ inch} = 4 \text{ feet}
\]

2. 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.