2025 AMC 8 Problem 24

In trapezoid ABCD, angles B and C measure 60^\circ and AB = DC. The side lengths are all positive integers and the perimeter of ABCD is 30 units. How many non-congruent trapezoids satisfy all of these conditions?

\textbf{(A)} 0 \qquad \textbf{(B)} 1 \qquad \textbf{(C)} 2 \qquad \textbf{(D)} 3 \qquad \textbf{(E)} 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.