¶ 2017 AMC 10B Problem 15
Problem:
Rectangle has and . Point is the foot of the perpendicular from to diagonal . What is the area of ?
Answer Choices:
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B.
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E.
Solution:
Triangles and have the same area because they share the base and, by symmetry, they have the same height. By the Pythagorean Theorem, . Because , the ratio of their areas is the square of the ratio of their corresponding sides. Their hypotenuses have lengths and , respectively, so their areas are in the ratio to . The area of is half that of the rectangle, so the area of is . Thus the area of is also .
The problems on this page are the property of the MAA's American Mathematics Competitions