AMC 12 2025b 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?

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