Problem:
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is . What is the greatest possible perimeter of the triangle?
Answer Choices:
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Solution:
Let the sides of the triangle have lengths , and . The Triangle Inequality implies that , so . Because is an integer, the greatest possible perimeter is .
The problems on this page are the property of the MAA's American Mathematics Competitions