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
