Difference between revisions of "2001 AMC 12 Problems/Problem 10"
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The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to | The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to | ||
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+ | <math> \text{(A) }50 \qquad \text{(B) }52 \qquad \text{(C) }54 \qquad \text{(D) }56 \qquad \text{(E) }58 </math> | ||
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== Solution == | == Solution == |
Revision as of 00:47, 17 January 2021
- The following problem is from both the 2001 AMC 12 #10 and 2001 AMC 10 #18, so both problems redirect to this page.
Problem
The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to
Solution
Consider any single tile:
If the side of the small square is , then the area of the tile is , with covered by squares and by pentagons. Hence exactly of any tile are covered by pentagons, and therefore pentagons cover of the plane. When expressed as a percentage, this is , and the closest integer to this value is .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 AMC 12 Problems and Solutions |
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.