The parallel sides of a trapezoid are 3 and 9. The non-parallel sides are 4 and 6. A line parallel to the bases divides the trapezoid into two trapezoids of equal perimeters. The ratio in which each of the non-parallel sides is divided is:
[asy]defaultpen(linewidth(.8pt));
unitsize(2cm);pair A = origin;
pair B = (2.25,0);
pair C = (2,1);
pair D = (1,1);
pair E = waypoint(A--D,0.25);
pair F = waypoint(B--C,0.25);draw(A--B--C--D--cycle);
draw(E--F);label("6",midpoint(A--D),NW);
label("3",midpoint(C--D),N);
label("4",midpoint(C--B),NE);
label("9",midpoint(A--B),S);[/asy]<spanclass=′latex−bold′>(A)</span> 4:3<spanclass=′latex−bold′>(B)</span> 3:2<spanclass=′latex−bold′>(C)</span> 4:1<spanclass=′latex−bold′>(D)</span> 3:1<spanclass=′latex−bold′>(E)</span> 6:1 geometrytrapezoidratiosimilar triangles