In rectangle ABCD, points F and G lie on AB so that AF \equal{} FG \equal{} GB and E is the midpoint of DC. Also, AC intersects EF at H and EG at J. The area of the rectangle ABCD is 70. Find the area of triangle EHJ.
[asy]
size(180);
pair A, B, C, D, E, F, G, H, J;
A = origin;
real length = 6;
real width = 3.5;
B = length*dir(0);
C = (length, width);
D = width*dir(90);
F = length/3*dir(0);
G = 2*length/3*dir(0);
E = (length/2, width);
H = extension(A, C, E, F);
J = extension(A, C, E, G);draw(A--B--C--D--cycle);
draw(G--E--F);
draw(A--C);label("A", A, dir(180));
label("D", D, dir(180));
label("B", B, dir(0));
label("C", C, dir(0));
label("F", F, dir(270));
label("E", E, dir(90));
label("G", G, dir(270));
label("H", H, dir(140));
label("J", J, dir(340));
[/asy]
<spanclass=′latex−bold′>(A)</span> 25<spanclass=′latex−bold′>(B)</span> 1235<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 27<spanclass=′latex−bold′>(E)</span> 835 geometryrectangleanalytic geometrylinear algebramatrixratiotrigonometry