Isoceles $\triangle ABC$ has equal side lengths $AB$ and $BC$. In the figure below, segments are drawr 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 of $h$ of $\triangle ABC$?

A. 14.6

B. 14.8

C. 15

D. 15.2

E. 15.4