2006 AMC 10 #12
Source:
August 20, 2011
geometry
Problem Statement
Rolly wishes to secure his dog with an 8-foot rope to a square shed that is 16 feet on each side. His preliminary drawings are shown. Which of these arrangements gives the dog the greater area to roam, and by how many square feet?[asy]defaultpen(linewidth(0.7));
size(7cm);
D((0,0)--(16,0)--(16,-16)--(0,-16)--cycle, black);
D((16,-8)--(24,-8), black);
label('Dog', (24, -8), SE);
label('I', (8,-8), (0,0));
MP('8', (16,-4), W);
MP('8', (16,-12),W);
MP('8', (20,-8), N);
label('Rope', (20,-8),S);
D((0,-20)--(16,-20)--(16,-36)--(0,-36)--cycle, black);
D((16,-24)--(24,-24), black);
label("II", (8,-28), (0,0));
MP('4', (16,-22), W);
MP('8', (20,-24), N);
label("Dog",(24,-24),SE);
label("Rope", (20,-24), S);
dot((24,-24)^^(24,-8));[/asy]