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?

Rationale

The actual length of a side of the square region is 1.5 miles.

To find the actual length of a side of the square region, we first calculate the square's perimeter in inches, which is 6 inches. Since 1/4 inch on the map corresponds to 1 mile, we find the length of one side of the square by dividing the perimeter by 4 (the number of sides), and then converting that measurement to miles.

A (1.5) YOUR ANSWER

This choice is incorrect because 1.5 miles is actually the correct calculation for the length of one side of the square region. The calculated length of one side is obtained by converting the total perimeter into miles correctly.

B (3) YOUR ANSWER

This choice is incorrect because if the perimeter of the square is 6 inches, each side of the square would be 1.5 inches (6 inches divided by 4). When converted to miles (1.5 inches multiplied by 4 to equal 1 mile), it does not yield 3 miles.

C (6) CORRECT

This choice is incorrect because if one side were 6 miles, the perimeter would be 24 miles (6 miles multiplied by 4). However, the perimeter is given as 6 inches, which does not support this value.

D (24) YOUR ANSWER

This choice is incorrect because 24 miles would imply an unrealistically large square for a 6-inch perimeter. The conversion from inches to miles shows that the actual side length is 1.5 miles, not 24.

Conclusion

The problem requires understanding the relationship between inches on the map and actual miles. The perimeter of 6 inches represents a square where each side is calculated to be 1.5 inches, translating to an actual length of 1.5 miles per side. The choices presented reflect misunderstandings of perimeter-to-length calculations and the conversion between map measurements and real distances.

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?

The actual length of a side of the square region is 1.5 miles.

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