In rectangle P Q R S, P Q=8 and Q R=6. Points A and B lie on \overline{P Q}, points C and D lie on \overline{Q R}, points E and F lie on \overline{R S}, and points G and H lie on \overline{S P} so that A P=B Q<4 and the convex octagon A B C D E F G H is equilateral. The length of a side of this octagon can be expressed in the form k+m \sqrt{n}, where k, m, and n are integers and n is not divisible by the square of any prime. What is k+m+n ?

**Answer Choices**

A. 1

B. 7

C. 21

D. 92

E. 106