The shortest side of a triangle ABC is half of the second side and a third of the longest side how does the perimeter of the triangle compared to the longest side

First of all, lets say a is the shortest side, b the second and c the longest. We can therefore write the following equations: a = (1/2) b = (1/3) c - > b=2a and c=3a (in order to have the three of them with the same variable) Perimeter = a + b + c P = a + 2a + 3a P=6a Now if we compare c to the perimeter (using ratio) we get: c/6a = 3a/6a = 1/2 Therefore, the longest side is equal to half the perimeter