Answer
Use indirect logic.
Work Step by Step
Assume there is a triangle with a perimeter which is twice the length of its longest side. First, draw a straight line, which represents the longest side. The shortest distance between the two end points is a straight line. This would add up to be twice the length of the longest side. However, a triangle cannot be formed using this, for the two additional sides cannot directly connect the two end points of the initial line. Thus, we conclude that the perimeter of a triangle cannot be twice the length of its longest side.
