2021 AMC 12B Problems/Problem 14
Contents
[hide]Problem
Let be a rectangle and let be a segment perpendicular to the plane of . Suppose that has integer length, and the lengths of and are consecutive odd positive integers (in this order). What is the volume of pyramid
Solution
Solution 1
This question is just about pythagorean theorem With these calculation, we find out answer to be ~Lopkiloinm
Solution 2
Let be , be , be , , , be , , respectively.
We have three equations:
Subbing in the first and third equation into the second equation, we get: Therefore, , Solving for other values, we get , . The volume is then ~jamess2022(burntTacos)
Video Solution by Hawk Math
https://www.youtube.com/watch?v=p4iCAZRUESs
See Also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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All AMC 12 Problems and Solutions |
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