2017 AMC 8 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}\qquad\textbf{(B) }\frac{3}{2}\qquad\textbf{(C) }2\qquad\textbf{(D) }\frac{12}{5}\qquad\textbf{(E) }\frac{5}{2}

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