For reasons too complicated to explain, I need to create a rectangular orchid garden with an ares of exactly 324 square feet abutting my house so that the house itself forms the northern boundary. The...

For reasons too complicated to explain, I need to create a rectangular orchid garden with an ares of exactly 324 square feet abutting my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the east and west sides costs $2 per foot. What are the dimensions of the orchid garden with the least expensive fence?