AMC 8 2004 Problem 24
Source:
July 22, 2011
siukkduilykgjk
Problem Statement
In the figure, is a rectangle and is a parallelogram. Using the measurements given in the figure, what is the length of the segment that is perpendicular to and ?[asy]
defaultpen(linewidth(0.8));
size(200);
pair A=(0,8), B=(10,8), C=(10,0), D=origin;
pair E=(4,8), F=(10,3), G=(6,0), H=(0,5);
pair I=H+4*dir(H--E);
pair J=foot(I, F, G);draw(A--B--C--D--cycle);
draw(E--F--G--H--cycle);
draw(I--J);
draw(rightanglemark(H,I,J));
draw(rightanglemark(F,J,I));label("", A, dir((5,4)--A));
label("", B, dir((5,4)--B));
label("", C, dir((5,4)--C));
label("", D, dir((5,4)--D));
label("", E, dir((5,4)--E));
label("", F, dir((5,4)--F));
label("", G, dir((5,4)--G));
label("", H, dir((5,4)--H));
label("", I--J, SW);label("3", H--A, W);
label("4", E--A, N);
label("6", E--B, N);
label("5", F--B, dir(1));
label("3", F--C, dir(1));
label("5", H--D, W);
label("4", C--G, S);
label("6", D--G, S);
[/asy]