The perimeter of a rectangular flower garden is 21 feet. This garden is to be built on the side of a hill meaning that one of the longer sides of the flower garden requires three times as much material to build as compared to the other longer side. If the building materials cost $1 per foot and the total cost to build the perimeter of the flower garden is $35, what are the dimensions of the garden? Define variables, set up a system of equations, and solve them using algebraic methods.