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?

So triangle has 3 sides
represent them as x,y,z
so lets say x=shortest side
y=2nd side
z=longest side

x is 1/2 of the second side
x=1/2(y)

shortest side is 1/3 of the longset side
x=1/3(z)
how does the triangle compart the longest side (z)

x+y+z=perimiter
solve to subsitute and convert all values to z
x=1/2y
2x=y
2(1/3z)=y
2/3(z)=y
and x=1/3(z)
therefor, subsitute so that there are only z terms
 1/3(z)+2/3(z)+z=perimiter
add like terms
3/3(z)+z=p
z+z=p
2z=p
the peimiter is 2 times of the longest side