To convert the dimensions from the original scale of \(2 \text{ in.} = 3 \text{ ft}\) to the new scale of \(4 \text{ in.} = 5 \text{ ft}\), we will follow these steps.
Part 1: First Step
The correct first step in finding the dimensions of the new scale is:
C. Multiply each dimension on the scale drawing by \( \frac{5 \text{ ft}}{4 \text{ in.}} \) to find the actual dimension of the patio.
This is because we want to find the actual dimensions based on the new scale, and that ratio translates the scale drawing (in inches) to actual dimensions (in feet).
Part 2: Finding the Length and Width with the New Scale
Given Dimensions
- Length on original blueprint: 28 in.
- Width on original blueprint: 26 in.
Now, using the scale conversion:
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Convert the length: \[ \text{Actual length} = 28 \text{ in.} \times \frac{5 \text{ ft}}{4 \text{ in.}} = 28 \times \frac{5}{4} = 35 \text{ ft} \]
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Convert the width: \[ \text{Actual width} = 26 \text{ in.} \times \frac{5 \text{ ft}}{4 \text{ in.}} = 26 \times \frac{5}{4} = 32.5 \text{ ft} \]
Conclusion
- The length of the blueprint with the new scale is 35 ft.
- The width of the blueprint with the new scale is 32.5 ft.
If you're specifically looking for the length in inches for the new blueprint, considering \(35 \text{ ft} = 35 \times 12 = 420 \text{ in}\). So:
- The length of the blueprint with the new scale is 420 in.