Difference between revisions of "2025 AIME I Problems/Problem 12"
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+ | ==Problem== | ||
+ | The set of points in <math>3</math>-dimensional coordinate space that lie in the plane <math>x+y+z=75</math> whose coordinates satisfy the inequalities <cmath>x-yz<y-zx<z-xy</cmath>forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form <math>a\sqrt{b},</math> where <math>a</math> and <math>b</math> are positive integers and <math>b</math> is not divisible by the square of any prime. Find <math>a+b.</math> | ||
+ | ==See also== | ||
+ | {{AIME box|year=2025|num-b=11|num-a=13|n=I}} | ||
+ | |||
+ | {{MAA Notice}} |
Revision as of 20:07, 13 February 2025
Problem
The set of points in -dimensional coordinate space that lie in the plane
whose coordinates satisfy the inequalities
forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form
where
and
are positive integers and
is not divisible by the square of any prime. Find
See also
2025 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.