AMC 12B 2025 (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?

\text{(A)}\;20

\text{(B)}\;22

\text{(C)}\;24

\text{(D)}\;26

\text{(E)}\;28