Question

Select the two correct answers.
A rectangular field has whole number dimensions.

The length is 11 miles.
The width is less than the length.
What are the two possible areas of the field?

112 square miles
45 square miles
93 square miles
195 square miles
120 square miles

Answer 1

To find the possible areas of the rectangular field, we need to use the formula for the area of a rectangle, which is:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Given that the length is 11 miles and the width is a whole number less than the length, the possible widths can be any whole number from 1 to 10 miles. We can compute the area for each of these widths:

1. Width = 1: Area = \( 11 \times 1 = 11 \) square miles
2. Width = 2: Area = \( 11 \times 2 = 22 \) square miles
3. Width = 3: Area = \( 11 \times 3 = 33 \) square miles
4. Width = 4: Area = \( 11 \times 4 = 44 \) square miles
5. Width = 5: Area = \( 11 \times 5 = 55 \) square miles
6. Width = 6: Area = \( 11 \times 6 = 66 \) square miles
7. Width = 7: Area = \( 11 \times 7 = 77 \) square miles
8. Width = 8: Area = \( 11 \times 8 = 88 \) square miles
9. Width = 9: Area = \( 11 \times 9 = 99 \) square miles
10. Width = 10: Area = \( 11 \times 10 = 110 \) square miles

Now, let's check which of these areas are among the options provided: 112, 45, 93, 195, 120 square miles.

From our calculations, the areas produced by the widths (1 to 10 miles) are 11, 22, 33, 44, 55, 66, 77, 88, 99, and 110 square miles.

None of these match the options given, but we need to ensure if we missed any possible combinations:

The area options are:

- 112 square miles (not possible)
- 45 square miles (not possible)
- 93 square miles (not possible)
- 195 square miles (not possible)
- 120 square miles (not possible)

Thus, there actually are no areas from our calculations that match the provided options.

However, if we stick strictly to the calculations we have done, we see that none of the areas above can be correct given the constraints of a whole number width under 11.

In conclusion, there appears to have been a misunderstanding in interpreting the problem as the given options do not align with the calculated areas for a field that meets the stated criteria. We can attempt to clarify or confirm the context but if strictly adhering to whole number dimensions under 11, none of the areas in the provided list are possible.