Final answer:
The city will need approximately 4 miles of fencing for the expanded park after multiplying the original perimeter by the square root of the factor by which the park's size is increased (2.5). The provided answer choices A) 6.25 miles, B) 7.5 miles, C) 8.75 miles, D) 10 miles do not match the correct calculation, suggesting an error in the question or answer choices.
Step-by-step explanation:
To determine the amount of fencing needed for the expanded park, we need to consider how the rectangular park's dimensions will affect the perimeter when the park's size is increased by a multiple. The initial perimeter of the park is 2.5 miles. When the park is expanded to 2.5 times its original size, this scaling affects the dimensions linearly. Therefore, both the length and width of the park will be scaled up by the square root of 2.5 to maintain the same aspect ratio.
Since the perimeter is a linear measurement, we then multiply the original perimeter by the square root of 2.5 to get the new perimeter:
New perimeter = Original perimeter × √(Scaling factor)
New perimeter = 2.5 miles × √2.5
Using a calculator, the square root of 2.5 is approximately 1.5811, so:
New perimeter = 2.5 miles × 1.5811 = 3.95275 miles.
Therefore, the city will need approximately 4 miles of fencing to go around the expanded park, which is not exactly any of the answer choices (A) 6.25 miles, (B) 7.5 miles, (C) 8.75 miles, or (D) 10 miles. The question or the answer choices seem to be erroneous. Based on the provided calculation method, none of these answers are correct. Typically, you would expect an increased perimeter due to the increased size, but the exact answer will depend on the correct interpretation of '2.5 times its current size'.