Problem:
Each side of the large square in the figure is trisected (divided into three equal parts). The corners of an inscribed square are at these trisection points, as shown. The ratio of the area of the inscribed square to the area of the large square is
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Answer Choices:
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Solution:
Taking the side of the large square to be inches gives an area of square inches. Each of the four right triangles has an area of sq. inch. The area of the inscribed square is the area of the large square minus the area of the four right triangles, that is, sq. inches. The desired ratio is .
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Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions