2024 AMC 8 Problem 20
Attempt Problem 20 of the 2024 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
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?
Answer: D
Small hint:
An equilateral triangle through must use face diagonals from
Big hint:
Look at the three vertices a face diagonal away from
Solution:
We first note that we can only form equilateral triangles if we go through the diagonals of the square faces, otherwise at least one angle of the triangle will be different. Afterwards, it is easy to exhaust all possible equilateral triangles that can be formed: and
Thus, D is the correct answer.
Problem 20 in other years
- 1985 AMC 8
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