A rectangular piece of paper with a pink front and black back has side lengths in direct proportion to the numbers 3 and 5.
When this paper is folded along the dashed line passing through vertex B as shown in the figure, vertex C comes onto side AD.
Accordingly, what is the ratio of the area of the black triangle formed in Figure 2 to the area of the pink rectangle in Figure 1?
A) $\frac{1}{18}$
B) $\frac{5}{18}$
C) $\frac{5}{9}$
D) $\frac{3}{8}$
E) $\frac{5}{8}$