1. On a county map, 1/4 inch represents 1 mile. If a square region on the map has a perimeter of 6 inches, what is the actual length of a side of the square region, in miles?
Answer: C
The actual length of a side of the square region is 1.5 miles.
Given that 1/4 inch represents 1 mile, we can determine the actual dimensions of the square region. The perimeter of the square is 6 inches, which means each side measures 6 inches divided by 4, resulting in 1.5 miles per side.
A) 1.5
This option correctly calculates the length of a side of the square region. Since the perimeter is 6 inches, each side is 6 inches divided by 4, which equals 1.5 miles.
B) 3
This option is incorrect because it suggests that each side of the square measures 3 miles. However, with a perimeter of 6 inches, each side must be shorter, specifically 1.5 miles.
C) 6
This choice is incorrect as it implies each side is 6 miles long. Given the perimeter of 6 inches, this calculation does not align with the conversion of inches to miles based on the provided scale.
D) 24
This option is also incorrect. A side length of 24 miles is not feasible since the perimeter is only 6 inches, which does not correspond to such a large measurement when converted to miles.
Conclusion
The correct answer is 1.5 miles, as each side of the square region must be calculated from the total perimeter of 6 inches divided by 4. All other options incorrectly represent the length of a side based on the given perimeter and scale, demonstrating a misunderstanding of the conversion between inches and miles.