Difference between revisions of "2006 AMC 10B Problems/Problem 10"
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The lengths of the sides are: <math>x</math>, <math>3x</math>, and <math>15</math>. | The lengths of the sides are: <math>x</math>, <math>3x</math>, and <math>15</math>. | ||
− | By the | + | By the [[Triangle Inequality]], |
<math> 3x < x + 15 </math> | <math> 3x < x + 15 </math> |
Revision as of 00:47, 14 July 2006
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?
Solution
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