¶ 2015 AMC 10B Problem 13
Problem:
The line forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?
Answer Choices:
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Solution:
Label the vertices of the triangle , and . By the Pythagorean Theorem . Two altitudes are and . Let be the third altitude. The area of this triangle is , so . Therefore . The sum of the lengths of the altitudes is .
The problems on this page are the property of the MAA's American Mathematics Competitions