Let A B C D be a parallelogram with area 15 . Points P and Q are the projections of A and C, respectively, onto the line B D; and points R and S are the projections of B and D, respectively, onto the line A C. See the figure, which also shows the relative locations of these points.
Suppose P Q=6 and R S=8, and let d denote the
length of \overline{B D}, the longer diagonal of A B C D. Then d^{2} can be written in the form m+n \sqrt{p}, where m, n, and p are positive integers and p is not divisible by the square of any prime. What is m+n+p ?
Answer Choices
A. 81
B. 89
C. 97
D. 105
E. 113