Problem:
Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia's trip was, compared to Jerry's trip?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the square had side length , then Jerry's path had length , and Silvia's path along the diagonal, by the Pythagorean Theorem, had length . Therefore Silvia's trip was shorter by
, and the required percentage is
The closest of the answer choices is .
The problems on this page are the property of the MAA's American Mathematics Competitions