Answer:
17.89 miles long.
Explanation:
The pedestrian route that runs diagonally across the rectangular park is the hypotenuse of a right triangle whose legs are the length and width of the park. We can use the Pythagorean theorem to find the length of this diagonal route.
According to the Pythagorean theorem, the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of its legs. In this case, one leg of the right triangle is 16 miles long and the other leg is 8 miles long. So, we have:
d² = 16² + 8²
d² = 256 + 64
d² = 320
d = √320
d ≈ 17.89
So, the pedestrian route that runs diagonally across the park is approximately 17.89 miles long.