Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2024 AMC 8 Problems/Problem 6

Revision as of 17:11, 25 January 2024 by Blueprimes (talk | contribs) (→‎Solution 1 (Analysis))

Solution 1 (Analysis)

$R$ skips around the boundary of the rink, while $P$ goes around the whole boundary. Hence, the length of path $R$ is less than the length of path $P$. 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 $S$ is longer than $P$. Finally, each V-shaped zag path from path $Q$ is longer than a diagonal in path $S$, so the length of path $Q$ is greater than that of $S$. Collectively, we obtain the answer $\boxed{\textbf{(D)}~R, P, S, Q}$.

Video Solution 1(easy to digest) by Power Solve

https://yo

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2024_AMC_8_Problems/Problem_6&oldid=212923"