There are repeaters that you can get from the usual places (NewEgg, Amazon, etc.) that act as a powered buffer to allow the line to be extended. A friend of mine runs his Drobo about 30 feet away by using at least one of these. He uses it for media storage and is very happy.
Yes, that ought to work. The fact that it’s a repeater makes it active (it does something). The little box at the middle is the “guts” (the active repeater part) so you know it’s not just a “simple” cable.