2023 AMC 8 Problem 24

Isosceles triangle ABC has equal side lengths AB and BC. In the figures below, segments are drawn parallel to \overline{AC} so that the shaded portions of \triangle ABC have the same area. The heights of the two unshaded portions are 11 and 5 units, respectively. What is the height h of \triangle ABC?

\textbf{(A)} 14.6 \qquad \textbf{(B)} 14.8 \qquad \textbf{(C)} 15 \qquad \textbf{(D)} 15.2 \qquad \textbf{(E)} 15.4

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