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2024 AMC 10 Problems/Problem 15

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Problem

Let $a$ , $b$ , and $c$ be positive integers such that $a^2 + b^2 = c^2$ . What is the least possible value of $a + b + c$ such that $a$ , $b$ , and $c$ form a non-degenerate triangle?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 25$

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