Difference between revisions of "2024 AMC 8 Problems/Problem 20"
| Line 29: | Line 29: | ||
https://www.youtube.com/watch?v=Xg-1CWhraIM | https://www.youtube.com/watch?v=Xg-1CWhraIM | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2024|num-b=19|num-a=21}} | ||
| + | {{MAA Notice}} | ||
Revision as of 20:08, 26 January 2024
Contents
Problem
Any three vertices of the cube 
, shown in the figure below, can be connected to form a triangle. (For example, vertices 
, 
, and 
can be connected to form isosceles 
.) How many of these triangles are equilateral and contain as a vertex?
Solution 1
The only equilateral triangles that can be formed are through the diagonals of the faces of the square with length 
. From P you have 
possible vertices that are possible to form a diagonal through one of the faces. So there are possible triangles. So the answer 
~Math 645
~andliu766
Video Solution by Power Solve
https://www.youtube.com/watch?v=7_reHSQhXv8
Video Solution 1 by Math-X (First understand the problem!!!)
~Math-X
Video Solution 2 by OmegaLearn.org
Video Solution 3 by SpreadTheMathLove
https://www.youtube.com/watch?v=Svibu3nKB7E
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=Xg-1CWhraIM
See Also
| 2024 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
