AMC 10A 2025 (Problem 3)

Plane GeometryMedium
How many isosceles triangles are there with positive area whose side lengths are all positive integers and whose longest side has length 2025?
(A)  2025\text{(A)}\;2025(B)  2026\text{(B)}\;2026(C)  3012\text{(C)}\;3012(D)  3037\text{(D)}\;3037(E)  4050\text{(E)}\;4050