¶ 2008 AMC8 Problem 23
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Problem:
In square and . What is the ratio of the area of to the area of square
Answer Choices:
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E.
Solution:
Because the answer is a ratio, it does not depend on the side length of the square. Let and . That means square has side length and area square units. The area of is equal to the area of square units. Triangle is an isosceles right triangle with leg lengths . The area of is square units. The area of is equal to the area of the square minus the areas of the three right triangles: . So the ratio of the area of to the area of square is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions