2024 AMC 8 Problems/Problem 6
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Solution 1 (Analysis)
skips around the boundary of the rink, while
goes around the whole boundary. Hence, the length of path
is less than the length of path
. Now, using the fact that the hypotenuse of a right triangle is greater than both of its legs, it is clear that the path described in
is longer than
. Finally, each V-shaped zag path from path
is longer than a diagonal in path
, so the length of path
is greater than that of
. Collectively, we obtain the answer
.