Difference between revisions of "2021 AMC 12B Problems/Problem 14"
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==Solution== | ==Solution== | ||
− | + | ===Solution 1=== | |
+ | This question is just about pythagorean theorem | ||
+ | <cmath>a^2+(a+2)^2-b^2 = (a+4)^2</cmath> | ||
+ | <cmath>2a^2+4a+4-b^2 = a^2+8a+16</cmath> | ||
+ | <cmath>a^2-4a+4-b^2 = 16</cmath> | ||
+ | <cmath>(a-2+b)(a-2-b) = 16</cmath> | ||
+ | <cmath>a=3, b=7</cmath> | ||
+ | With these calculation, we find out answer to be | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2021|ab=B|num-b=13|num-a=15}} | {{AMC12 box|year=2021|ab=B|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 22:59, 11 February 2021
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
See Also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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 AMC 12 Problems and Solutions |
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