The Relationship of Power and Heat to Length of a Resistor
The watt density is the power per unit surface area, determined over a vanishingly small area. 

Since the wires are the same diameter, and the same resistivity, to get a constant power per unit area, the voltage per unit length must be the same. 

Think about two exactly similar lengths of wire, powered, say, from 8.485V. Now connect them in series, and power them from a single supply.