Difference between revisions of "2024 AMC 8 Problems/Problem 6"
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==Solution 1 (Analysis)== | ==Solution 1 (Analysis)== | ||
− | <math>R</math> skips around the boundary of the rink, while <math>P</math> goes around the whole boundary. Hence, the length of path <math> | + | <math>R</math> skips around the boundary of the rink, while <math>P</math> goes around the whole boundary. Hence, the length of path <math>R</math> is less than the length of path <math>P</math>. 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 <math>S</math> is longer than <math>P</math>. Finally, each V-shaped zag path from path <math>Q</math> is longer than a diagonal in path <math>S</math>, so the length of path <math>Q</math> is greater than that of <math>S</math>. Collectively, we obtain the answer <math>\boxed{\textbf{(D)}~R, P, S, Q}</math>. |
==Video Solution 1(easy to digest) by Power Solve== | ==Video Solution 1(easy to digest) by Power Solve== | ||
https://yo | https://yo |
Revision as of 18:11, 25 January 2024
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
.