The shortest side of triangle ABC is half of the second side and a third of the longest side. How does the perimeter of the triangle compare to the longest side?

X = the shortest side of triangle ABC;

y = the second side of triangle ABC;

z = the longest site of triangle ABC;

P = the perimeter of triangle ABC;

x = (1 / 2) y;

x = (1 / 3) z;

Then (1 / 2) y = (1 / 3) z;

y = 2z / 3;

P = x + y + z = (1 / 3) z + 2z / 3 + z = z / 3 + 2z / 3 + z = 3z / 3 + z = z + z = 2z;

But 2z > z;

then, P > z;