Triangle A B C is equilateral with A B=1. Points E and G are on \overline{A C} and points D and F are on \overline{A B} such that both \overline{D E} and \overline{F G} are parallel to \overline{B C}. Furthermore, triangle A D E and trapezoids D F G E and F B C G all have the same perimeter. What is D E+F G ?
Answer Choices
A. 1
B. \dfrac{3}{2}
C. \dfrac{21}{13}
D. \dfrac{13}{8}
E. \dfrac{5}{3}
