2025 AMC 12B Problem 21

Two non-congruent triangles have the same area. Each triangle has sides of length 8 and 9, and the third side of each triangle has integer length. What is the sum of the lengths of the third sides?

\textbf{(A)} 20 \qquad \textbf{(B)} 22 \qquad \textbf{(C)} 24 \qquad \textbf{(D)} 26 \qquad \textbf{(E)} 28

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