Why 50 Ohms

The 50-Ohm compromise

The arithmetic mean between 30 ohms (best power handling) and 77 ohms (lowest loss) is 53.5, the geometric mean is 48 ohms. Thus the choice of 50 ohms is a compromise between power handling capability and signal loss per unit length, for air dielectric.

http://www.microwaves101.com/encyclopedia/why50ohms.cfm