Difference between revisions of "1986 AHSME Problems/Problem 6"

m (See also)
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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?
  
Solve <math>t</math> in this system of equation:
+
<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);
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label("$r$",(8.5,5.75));
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label("$s$",(22,5.75));
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</asy>
  
<cmath>t-w+l = 32\quad \\
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<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>
t-l+w = 28</cmath>
 
 
 
<math>\textbf{(A)}\ 28 \qquad
 
\textbf{(B)}\ 29 \qquad
 
\textbf{(C)}\ 30 \qquad
 
\textbf{(D)}\ 31 \qquad
 
\textbf{(E)}\ 32 </math>  
 
  
 
==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 $r$ is found to be $32$ inches. After rearranging the blocks as in Figure 2, length $s$ is found to be $28$ 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]

$\textbf{(A) }28\text{ inches}\qquad\textbf{(B) }29\text{ inches}\qquad\textbf{(C) }30\text{ inches}\qquad\textbf{(D) }31\text{ inches}\qquad\textbf{(E) }32\text{ inches}$

Solution

See also

1986 AHSME (ProblemsAnswer KeyResources)
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
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