Difference between revisions of "2024 AMC 10 Problems/Problem 15"
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Latest revision as of 19:48, 1 May 2025
Problem
Let ,
, and
be positive integers such that
. What is the least possible value of
such that
,
, and
form a non-degenerate triangle?
Solution
We know that represents a Pythagorean triple. The smallest Pythagorean triple is
.
To check if this forms a non-degenerate triangle, we verify the triangle inequality:
All inequalities hold, so is a valid solution.
Therefore, the least possible value of is
.