To determine how many rectangular lots of dimensions 120 yards by 60 yards can fit in a rectangular field of dimensions 900 yards by 240 yards, we can follow these steps:
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Calculate the area of the field: \[ \text{Area of the field} = \text{length} \times \text{width} = 900 , \text{yards} \times 240 , \text{yards} = 216000 , \text{square yards} \]
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Calculate the area of one lot: \[ \text{Area of one lot} = \text{length} \times \text{width} = 120 , \text{yards} \times 60 , \text{yards} = 7200 , \text{square yards} \]
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Determine how many lots can fit based on area: \[ \text{Number of lots} = \frac{\text{Area of the field}}{\text{Area of one lot}} = \frac{216000}{7200} = 30 \]
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Verify the fitting of the lots within the dimensions of the field:
- First, check how many lots fit along the length of the field (900 yards): \[ \frac{900}{120} = 7.5 \quad \text{(can fit 7 lots)} \]
- Next, check how many lots fit along the width of the field (240 yards): \[ \frac{240}{60} = 4 \quad \text{(can fit 4 lots)} \]
- Therefore, the total number of lots that can fit in the field is: \[ 7 \times 4 = 28 \]
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Try rotating the lots (if it can fit differently):
- Check how many lots fit along the length of the field with the lot dimensions switched (60 yards by 120 yards):
- Fit along the length (900 yards): \[ \frac{900}{60} = 15 \quad \text{(can fit 15 lots)} \]
- Fit along the width (240 yards): \[ \frac{240}{120} = 2 \quad \text{(can fit 2 lots)} \]
- Therefore, in this orientation: \[ 15 \times 2 = 30 \]
- Check how many lots fit along the length of the field with the lot dimensions switched (60 yards by 120 yards):
Conclusion: The total number of rectangular lots of dimensions 120 yards by 60 yards that can fit into the rectangular field is 30, by fitting the lots in the rotated configuration.
\[ \boxed{30} \]