To determine the correct statement about the change of scale, we first need to find out the scale for the original plan and the new plan based on the information given.
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Original Length: The original length of the courtyard is 54 feet, which corresponds to 18 inches in the drawing.
- Scale Calculation: \[ \text{Scale for original length} = \frac{\text{Actual Length (feet)}}{\text{Drawing Length (inches)}} = \frac{54 \text{ feet}}{18 \text{ inches}} = 3 \text{ feet per inch} \]
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New Length: The new length of the courtyard is 72 feet.
- Scale Calculation: \[ \text{Scale for new length} = \frac{\text{Actual Length (feet)}}{\text{Drawing Length (inches)}} = \frac{72 \text{ feet}}{18 \text{ inches}} = 4 \text{ feet per inch} \]
Now, let’s analyze the statements provided in the question:
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One inch represented 1 foot in the first scale, but now 1 inch represents 4 feet in the second scale. (This is incorrect; it was 3 feet in the first scale.)
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One inch represented 4 feet in the first scale, but now 1 inch represents 3 feet in the second scale. (This is incorrect; it was 3 feet in the first scale and 4 feet in the second scale.)
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One inch represented 54 feet in the first scale, but now 1 inch represents 72 feet in the second scale. (This is incorrect; the representation was in feet per inch.)
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One inch represented 3 feet in the first scale, but now 1 inch represents 4 feet in the second scale. (This is correct.)
Thus, the true statement about the change of scale is:
One inch represented 3 feet in the first scale, but now 1 inch represents 4 feet in the second scale.