Math Gold Medalist

Lor

2024 AMC 8 

Problem 6

Sergai skated around an ice rink, gliding along different paths. The gray lines in the figures below show foru of the paths labeled $P$, $Q$, $R$, and $S$. What is the sorted order of the four paths from shortest to longest?

[DIAGRAM]

$\textbf{(A)}\ P,Q,R,S \qquad \textbf{(B)}\ P,R,S,Q \qquad \textbf{(C)}\ Q,S,P,R \qquad \textbf{(D)}\ R,P,S,Q \qquad \textbf{(E)}\ R,S,P,Q$

Triangle Inequality

Pythagorean Theorem

First check R and P

Then check P and S

.

   Solution