Two Identical Blocks of Wood
Source:
November 6, 2005
Problem Statement
Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length is found to be inches. After rearranging the blocks as in Figure 2, length is found to be inches. How high is the table?[asy]
size(300);
defaultpen(linewidth(0.8)+fontsize(13pt));
path table = origin--(1,0)--(1,6)--(6,6)--(6,0)--(7,0)--(7,7)--(0,7)--cycle;
path block = origin--(3,0)--(3,1.5)--(0,1.5)--cycle;
path rotblock = origin--(1.5,0)--(1.5,3)--(0,3)--cycle;
draw(table^^shift((14,0))*table);
filldraw(shift((7,0))*block^^shift((5.5,7))*rotblock^^shift((21,0))*rotblock^^shift((18,7))*block,gray);
draw((7.25,1.75)--(8.5,3.5)--(8.5,8)--(7.25,9.75),Arrows(size=5));
draw((21.25,3.25)--(22,3.5)--(22,8)--(21.25,8.25),Arrows(size=5));
unfill((8,5)--(8,6.5)--(9,6.5)--(9,5)--cycle);
unfill((21.5,5)--(21.5,6.5)--(23,6.5)--(23,5)--cycle);
label("",(8.5,5.75));
label("",(22,5.75));
[/asy]