MathDB

6

Part of 1986 AMC 12/AHSME

Problems(1)

Two Identical Blocks of Wood

Source:

11/6/2005
Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length rr is found to be 3232 inches. After rearranging the blocks as in Figure 2, length ss is found to be 2828 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("rr",(8.5,5.75)); label("ss",(22,5.75)); [/asy]
<spanclass=′latex−bold′>(A)</span>28 inches<spanclass=′latex−bold′>(B)</span>29 inches<spanclass=′latex−bold′>(C)</span>30 inches<spanclass=′latex−bold′>(D)</span>31 inches<spanclass=′latex−bold′>(E)</span>32 inches<span class='latex-bold'>(A) </span>28\text{ inches}\qquad<span class='latex-bold'>(B) </span>29\text{ inches}\qquad<span class='latex-bold'>(C) </span>30\text{ inches}\qquad<span class='latex-bold'>(D) </span>31\text{ inches}\qquad<span class='latex-bold'>(E) </span>32\text{ inches}