Art of Problem Solving

2025 AMC 10A Problems/Problem 3

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How many isosceles triangles are there with positive area whose side lengths are all positive integers and whose longest side has length $2025$?

$\textbf{(A)}~2025\qquad\textbf{(B)}~2026\qquad\textbf{(C)}~3012\qquad\textbf{(D)}~3037\qquad\textbf{(E)}~4050$