Question 5598
Congratulations!  You are correct.

You can use the Pythagorean theorem to solve this because if you connect the center of town with the point 14 miles south of town and the point 10 miles west of town, you will have two legs of a right triangle.  The new road would constitute the hypotenuse of this right triangle.

So, if x is the length of the new road, then:
{{{x = sqrt(10^2 + 14^2)}}}
{{{x = sqrt(296)}}}
x = 17.2 miles.