AMC 8 2017 Problem 16

In the figure below, choose point $D$ on $\overline{BC}$ so that $\triangle ACD$ and $\triangle ABD$ have equal perimeters. What is the area of $\triangle ABD$?

$\textbf{(A) }\frac{3}{4} \textbf{(B) }\frac{3}{2} \textbf{(C) }2 \textbf{(D) }\frac{12}{5} \textbf{(E) }\frac{5}{2}$