Difference between revisions of "1986 AHSME Problems/Problem 6"
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==Problem== | ==Problem== | ||
+ | Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length <math>r</math> is found to be <math>32</math> inches. After rearranging the blocks as in Figure 2, length <math>s</math> is found to be <math>28</math> 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("$r$",(8.5,5.75)); | ||
+ | label("$s$",(22,5.75)); | ||
+ | </asy> | ||
− | + | <math>\textbf{(A) }28\text{ inches}\qquad\textbf{(B) }29\text{ inches}\qquad\textbf{(C) }30\text{ inches}\qquad\textbf{(D) }31\text{ inches}\qquad\textbf{(E) }32\text{ inches}</math> | |
− | |||
− | |||
− | <math>\textbf{(A)}\ | ||
− | \textbf{(B)}\ | ||
− | \textbf{(C)}\ | ||
− | \textbf{(D)}\ | ||
− | \textbf{(E)}\ | ||
==Solution== | ==Solution== |
Revision as of 21:32, 24 December 2015
Problem
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?
Solution
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.