I assume they are 10". That is what my single axle 94 trailer has.
I'm not sure how closely you inspected things, but you may be able to save money by replacing just the parts that aren't functioning instead of the full backing plate. To get my brakes working I replaced the master cylinder (in the actuator), the brake lines, and the wheel cylinders (a part on the backing plate). That took care of everything that comes in contact with brake fluid. If your shoes are worn (the brake that was dragging for example), you should be able to get those from Napa or another autoparts store.
Here is where I got my wheel cylinder: http://www.pacifictrailers.com/boat-...acking-plates/