¶ 2011 AMC8 Problem 16
Problem:
Let be the area of a triangle with sides of length , and . Let be the area of a triangle with sides of length , and . What is the relationship between and
Answer Choices:
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Solution:
The altitude shown divides each triangle into two congruent right triangles. The hypotenuse of each right triangle is . In the horizontal leg of each right triangle is , so the vertical leg is . In the horizontal leg of each right triangle is , so the vertical leg is . The area of is , and the area of is , so the two areas are equal.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions