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 15 . What is the greatest possible perimeter of the triangle?
Answer Choices:
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Solution:
The sides of the triangle are , and 15 for some positive integer . By the Triangle Inequality, these three numbers are the sides of a triangle if and only if and . Because is an integer, the first inequality is equivalent to , and the second inequality is equivalent to . Thus the greatest possible perimeter is .
The problems on this page are the property of the MAA's American Mathematics Competitions