Difference between revisions of "1994 AHSME Problems/Problem 2"
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--Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | ||
+ | |||
+ | ==Solution 2== | ||
+ | |||
+ | <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 CH=C--H; | ||
+ | path BF=B--F; | ||
+ | path FC=F--C; | ||
+ | path DH=D--H; | ||
+ | draw(A--B--C--D--cycle); | ||
+ | draw(EE--F); | ||
+ | draw(G--H); | ||
+ | draw(CH,L=Label("$b$",position=MidPoint,align=(0,1))); | ||
+ | draw(BF,L=Label("$y$",position=MidPoint,align=(1,0))); | ||
+ | draw(FC,L=Label("$x$",position=MidPoint,align=(1,0))); | ||
+ | draw(DH,L=Label("$a$",position=MidPoint,align=(0,1))); | ||
+ | label("$6$", (1.5,6)); | ||
+ | label("$14$", (6.5,6)); | ||
+ | label("$35$", (6.5,2.5)); | ||
+ | </asy> | ||
+ | |||
+ | In case its not immediately obvious from inspection what the dimensions of the small rectangles are, we can work it out. We know <math>ax</math> and <math>bx</math> and <math>by</math> and we want to know <math>ay</math>. We can compute it as follows <math>ay = \frac{(ax)(by)}{bx} = \frac{ 6\cdot 35 }{14} = 15</math> and the answer is <math>\fbox{B}</math> | ||
==See Also== | ==See Also== |
Latest revision as of 02:26, 28 May 2021
Contents
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?
Solution
We can easily see the dimensions of each small rectangle. So the area of the last rectangle is .
--Solution by TheMaskedMagician
Solution 2
In case its not immediately obvious from inspection what the dimensions of the small rectangles are, we can work it out. We know and and and we want to know . We can compute it as follows and the answer is
See Also
1994 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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.