Difference between revisions of "2021 AIME II Problems/Problem 5"

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==Problem==
 
==Problem==
These problems will not be posted until the 2021 AIME II is released on Thursday, March 25, 2021.
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For positive real numbers <math>s</math>, let <math>\tau(s)</math> denote the set of all obtuse triangles that have area <math>s</math> and two sides with lengths <math>4</math> and <math>10</math>. The set of all <math>s</math> for which <math>\tau(s)</math> is nonempty, but all triangles in <math>\tau(s)</math> are congruent, is an interval <math>a,b)</math>. Find <math>a^2+b^2</math>.
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==Solution==
 
==Solution==
 
We can't have a solution without a problem.
 
We can't have a solution without a problem.

Revision as of 14:31, 22 March 2021

Problem

For positive real numbers $s$, let $\tau(s)$ denote the set of all obtuse triangles that have area $s$ and two sides with lengths $4$ and $10$. The set of all $s$ for which $\tau(s)$ is nonempty, but all triangles in $\tau(s)$ are congruent, is an interval $a,b)$. Find $a^2+b^2$.

Solution

We can't have a solution without a problem.

See also

2021 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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