In diagram, point C is on side B D of quadrilateral A B D E. Also, A B and E D are perpendicular to B D, \angle A C B=60^{\circ}, \angle C A E=45^{\circ}, and \angle A E C=45^{\circ}. If A B=\sqrt{3}, what is the perimeter of quadrilateral A B D E ?
Answer Choices
A. 1+\sqrt{2}+2 \sqrt{3}
B. 2+2 \sqrt{2}+\sqrt{3}
C. 1+2 \sqrt{2}+2 \sqrt{3}
D. 2+\sqrt{2}+2 \sqrt{3}
E. 2+2 \sqrt{2}+2 \sqrt{3}