Difference between revisions of "2000 AIME I Problems/Problem 4"
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The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the perimeter of the rectangle. | The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the perimeter of the rectangle. | ||
| − | + | <center><asy>draw((0,0)--(69,0)--(69,61)--(0,61)--(0,0));draw((36,0)--(36,36)--(0,36)); | |
| + | draw((36,33)--(69,33));draw((41,33)--(41,61));draw((25,36)--(25,61)); | ||
| + | draw((34,36)--(34,45)--(25,45)); | ||
| + | draw((36,36)--(36,38)--(34,38)); | ||
| + | draw((36,38)--(41,38)); | ||
| + | draw((34,45)--(41,45));</asy></center> | ||
== Solution == | == Solution == | ||
Revision as of 01:59, 24 November 2007
Problem
The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the perimeter of the rectangle.
![[asy]draw((0,0)--(69,0)--(69,61)--(0,61)--(0,0));draw((36,0)--(36,36)--(0,36)); draw((36,33)--(69,33));draw((41,33)--(41,61));draw((25,36)--(25,61)); draw((34,36)--(34,45)--(25,45)); draw((36,36)--(36,38)--(34,38)); draw((36,38)--(41,38)); draw((34,45)--(41,45));[/asy]](http://latex.artofproblemsolving.com/d/8/1/d8140d628cc0905f333aa8deaface1b89ee6c983.png)
Solution
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See also
| 2000 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
