Let A B C D be a rectangle with A B=30 and B C=28. Points P and Q lie on \overline{B C} and \overline{C D}, respectively, so that all sides of \triangle A B P, \triangle P C Q, and \triangle Q D A have integer lengths. What is the perimeter of \triangle A P Q?
Answer Choices
A. 84
B. 86
C. 88
D. 90
E. 92