Difference between revisions of "1998 AJHSME Problems/Problem 13"
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* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
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Revision as of 23:29, 4 July 2013
Problem
What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale)
![[asy] draw((0,0)--(0,4)--(4,4)--(4,0)--cycle); draw((0,0)--(4,4)); draw((0,4)--(3,1)--(3,3)); draw((1,1)--(2,0)--(4,2)); fill((1,1)--(2,0)--(3,1)--(2,2)--cycle,black); [/asy]](http://latex.artofproblemsolving.com/5/9/b/59b849abaccf2ca59a38fc1cb6adf63f12eae897.png)
Solution
We can divide the large square into quarters by diagonals.
Then, in 
the area of the big square, the little square would have 
the area.
See also
| 1998 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
