2006 AMC 10B Problems/Problem 10
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?
Let be the length of the first side.
The lengths of the sides are: , , and .
By the triangle inequality:
The largest integer satisfing this inequality is
So the largest perimeter is