In the figure shown below, choose point D on side \overline{B C} so that \triangle A C D and \triangle A B D have equal perimeters. What is the area of \triangle A B D ?
Answer Choices
A. \dfrac{3}{4}
B. \dfrac{3}{2}
C. 2
D. \dfrac{12}{5}
E. \dfrac{5}{2}