Subject: Why do the permeability and permitivity of space coincide mathematically?

I understand the nature of electromagnetic waves (self-propagating perpendicular
magnetic and electric fields). I also understand how the permeability and
permitivity of free space affect magnetic and electric fields, respectively.
However, one divided by the square root of the product of the permeability of
free space and the permitivity of free space (1/sqrt(permeability*permitivity))
is equal to the speed of light (the units, Tm/A^2 and Nm^2/C^2 even end up
reducing to meters per second!) In terms of equations, why is this
mathematically in relationship to electromagnetic waves? Also, physically, why
does it work? It baffles even my physics teacher. 

Re: Why do the permeability and permitivity of space coincide mathematically?