In square ABCD, points P and Q lie on AD and AB, respectively. Segments BP and CQ intersect at right angles at R, with BR=6 and PR=7. What is the area of the square?[asy]
size(170);
defaultpen(linewidth(0.6));
real r = 3.5;
pair A = origin, B = (5,0), C = (5,5), D = (0,5), P = (0,r), Q = (5-r,0),
R = intersectionpoint(B--P,C--Q);
draw(A--B--C--D--A^^B--P^^C--Q^^rightanglemark(P,R,C,7));
dot("A",A,S);
dot("B",B,S);
dot("C",C,N);
dot("D",D,N);
dot("Q",Q,S);
dot("P",P,W);
dot("R",R,1.3*S);
label("7",(P+R)/2,NE);
label("6",(R+B)/2,NE);
[/asy]
<spanclass=′latex−bold′>(A)</span>85<spanclass=′latex−bold′>(B)</span>93<spanclass=′latex−bold′>(C)</span>100<spanclass=′latex−bold′>(D)</span>117<spanclass=′latex−bold′>(E)</span>125