Atriangle has a perimeter of 49 centimeters. each of the two longer sides of the triangle is three times as long as the shortest side. find the length of each side of the triangle

Two sides are 3x longer than the shortest side. So, set up your problem like this.
  X = unknown length in centimeters 
3X = length of two longer sides
1X = length of short side
3x + 3x + 1x = 49
7x  = 49 
x = 7
So, two longer sides are 21 centimeters each and the short side is 7 centimeters.
  21+21+7 = 49