2001 AMC 10 Problem 18

Problem 18 of 25IntermediateGeometry Combinatorics Arithmetic

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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Solution

Consider a repeating

3\times3

block of nine small squares. Four of these nine squares are not part of the pentagons, so the pentagons cover

1-\dfrac49=\dfrac59\approx55.6\%

of the area. This is closest to

56.

Thus, the correct answer is D.

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Tagged: area ratio · tiling · percentage

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