Difference between revisions of "1990 AJHSME Problems/Problem 3"
5849206328x (talk | contribs) (Created page with '==Problem== What fraction of the square is shaded? <asy> draw((0,0)--(0,3)--(3,3)--(3,0)--cycle); draw((0,2)--(2,2)--(2,0)); draw((0,1)--(1,1)--(1,0)); draw((0,0)--(3,3)); fill…') |
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{{AJHSME box|year=1990|num-b=2|num-a=4}} | {{AJHSME box|year=1990|num-b=2|num-a=4}} | ||
[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
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Latest revision as of 23:05, 4 July 2013
Problem
What fraction of the square is shaded?
![[asy] draw((0,0)--(0,3)--(3,3)--(3,0)--cycle); draw((0,2)--(2,2)--(2,0)); draw((0,1)--(1,1)--(1,0)); draw((0,0)--(3,3)); fill((0,0)--(0,1)--(1,1)--cycle,grey); fill((1,0)--(1,1)--(2,2)--(2,0)--cycle,grey); fill((0,2)--(2,2)--(3,3)--(0,3)--cycle,grey); [/asy]](http://latex.artofproblemsolving.com/9/4/1/9418063c2f79f6fd1e9f8ec5e2efe31f98590f2f.png)
Solution
Reflecting the square across the diagonal drawn, we see that the shaded region covers exactly the unshaded region in the original square, and thus makes up 
of the square 
.
See Also
| 1990 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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. 
