Difference between revisions of "1994 AHSME Problems/Problem 2"
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We can easily see the dimensions of each small rectangle. So the area of the last rectangle is <math>3\times 5=\boxed{\textbf{(B) }15}</math>. | We can easily see the dimensions of each small rectangle. So the area of the last rectangle is <math>3\times 5=\boxed{\textbf{(B) }15}</math>. | ||
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| + | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | ||
Revision as of 13:36, 28 June 2014
Problem
A large rectangle is partitioned into four rectangles by two segments parallel to its sides. The areas of three of the resulting rectangles are shown. What is the area of the fourth rectangle?
![[asy] draw((0,0)--(10,0)--(10,7)--(0,7)--cycle); draw((0,5)--(10,5)); draw((3,0)--(3,7)); label("6", (1.5,6)); label("?", (1.5,2.5)); label("14", (6.5,6)); label("35", (6.5,2.5)); [/asy]](http://latex.artofproblemsolving.com/3/1/f/31f1dc6fc961ef17ec97066f3f86050dca58b393.png)
Solution
![[asy] pair A=(0,0),B=(10,0),C=(10,7),D=(0,7),EE=(0,5),F=(10,5),G=(3,0),H=(3,7); path BG=shift(0,-0.5)*(B--G); path BF=shift(0.5,0)*(B--F); path FC=shift(0.5,0)*(F--C); path DH=shift(0,0.5)*(D--H); draw(A--B--C--D--cycle); draw(EE--F); draw(G--H); draw(BG,L=Label("$7$",position=MidPoint,align=(0,-1)),arrow=Arrows(),bar=Bars,red); draw(BF,L=Label("$5$",position=MidPoint,align=(1,0)),arrow=Arrows(),bar=Bars,red); draw(FC,L=Label("$2$",position=MidPoint,align=(1,0)),arrow=Arrows(),bar=Bars,red); draw(DH,L=Label("$3$",position=MidPoint,align=(0,1)),arrow=Arrows(),bar=Bars,red); label("$6$", (1.5,6)); label("$15$", (1.5,2.5),blue); label("$14$", (6.5,6)); label("$35$", (6.5,2.5)); [/asy]](http://latex.artofproblemsolving.com/9/b/1/9b1be94397c1f8fdf513d00d24423fdae84c4bb8.png)
We can easily see the dimensions of each small rectangle. So the area of the last rectangle is 
.
--Solution by TheMaskedMagician
