Two Trapezoids
Source:
June 8, 2009
geometrytrapezoidratiosimilar triangles
Problem Statement
The parallel sides of a trapezoid are and . The non-parallel sides are and . 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]