Question

A rectangular field is 900 yards by 240 yards. What is the greatest number of rectangular lots 120 yards by 60 yards that it can be divided into?

Answer 1

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:

1. **Calculate the area of the field**:
\[
\text{Area of the field} = \text{length} \times \text{width} = 900 \, \text{yards} \times 240 \, \text{yards} = 216000 \, \text{square yards}
\]

2. **Calculate the area of one lot**:
\[
\text{Area of one lot} = \text{length} \times \text{width} = 120 \, \text{yards} \times 60 \, \text{yards} = 7200 \, \text{square yards}
\]

3. **Determine how many lots can fit based on area**:
\[
\text{Number of lots} = \frac{\text{Area of the field}}{\text{Area of one lot}} = \frac{216000}{7200} = 30
\]

4. **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:
\[
7 \times 4 = 28
\]

5. **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:
\[
15 \times 2 = 30
\]

**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.

\[
\boxed{30}
\]