For reasons too complicated to explain, I need to create a rectangular orchid garden with an area of exactly 169sq. ft. abutting my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. What are the dimensions of the orchid garden with the least expensive fence?
south fence = ??? ft
east and west fences = ??? ft