In the figure, ABCD is a square of side length 1. The rectangles JKHG and EBCF are congruent. What is BE?
[asy]
unitsize(150);
pair A,B,C,D,E,F,G,H,J,K;
A=(1,0); B=(0,0); C=(0,1); D=(1,1);
draw(A--B--C--D--A);E=(2-sqrt(3),0); F=(2-sqrt(3),1);
draw(E--F);G=(1,sqrt(3)/2); H=(2.5-sqrt(3),1);
K=(2-sqrt(3),1-sqrt(3)/2); J=(0.5,0);
draw(G--H--K--J--G);label("A",A,SE);
label("B",B,SW);
label("C",C,NW);
label("D",D,NE);
label("E",E,S);
label("F",F,N);
label("G",G,E);
label("H",H,N);
label("K",K,W);
label("J",J,S);
[/asy]<spanclass=′latex−bold′>(A)</span>21(6−2)<spanclass=′latex−bold′>(B)</span>41<spanclass=′latex−bold′>(C)</span>2−3<spanclass=′latex−bold′>(D)</span>63<spanclass=′latex−bold′>(E)</span>1−22