Difference between revisions of "2012 AMC 8 Problems/Problem 5"
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In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is ,<math> X </math> in centimeters? | In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is ,<math> X </math> in centimeters? | ||
| − | + | <asy> | |
pair A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R; | pair A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R; | ||
A=(4,0); | A=(4,0); | ||
| Line 22: | Line 22: | ||
R=(4,3); | R=(4,3); | ||
draw(A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--cycle); | draw(A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--cycle); | ||
| − | label(" | + | label("$X$",(3.4,1.5)); |
label("6",(7.6,1.5)); | label("6",(7.6,1.5)); | ||
label("1",(7.6,3.5)); | label("1",(7.6,3.5)); | ||
| Line 38: | Line 38: | ||
label("2",(0.8,4.5)); | label("2",(0.8,4.5)); | ||
label("2",(1.5,3.8)); | label("2",(1.5,3.8)); | ||
| − | label("2",(2.8,2.6)); | + | label("2",(2.8,2.6));</asy> |
<math> \textbf{(A)}\hspace{.05in}1\qquad\textbf{(B)}\hspace{.05in}2\qquad\textbf{(C)}\hspace{.05in}3\qquad\textbf{(D)}\hspace{.05in}4\qquad\textbf{(E)}\hspace{.05in}5 </math> | <math> \textbf{(A)}\hspace{.05in}1\qquad\textbf{(B)}\hspace{.05in}2\qquad\textbf{(C)}\hspace{.05in}3\qquad\textbf{(D)}\hspace{.05in}4\qquad\textbf{(E)}\hspace{.05in}5 </math> | ||
Revision as of 14:18, 23 November 2012
In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is ,
in centimeters?
![[asy] pair A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R; A=(4,0); B=(7,0); C=(7,4); D=(8,4); E=(8,5); F=(10,5); G=(10,7); H=(7,7); I=(7,8); J=(5,8); K=(5,7); L=(4,7); M=(4,6); N=(0,6); O=(0,5); P=(2,5); Q=(2,3); R=(4,3); draw(A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--cycle); label("$X$",(3.4,1.5)); label("6",(7.6,1.5)); label("1",(7.6,3.5)); label("1",(8.4,4.6)); label("2",(9.4,4.6)); label("2",(10.4,6)); label("3",(8.4,7.4)); label("1",(7.5,7.8)); label("2",(6,8.5)); label("1",(4.7,7.8)); label("1",(4.3,7.5)); label("1",(3.5,6.5)); label("4",(1.8,6.5)); label("1",(-0.5,5.5)); label("2",(0.8,4.5)); label("2",(1.5,3.8)); label("2",(2.8,2.6));[/asy]](http://latex.artofproblemsolving.com/b/c/d/bcd57a9d78159bce4d3873f81f5d879beaed1d5a.png)
