If a a sheet of cardboard measures 9 feet by 6 feet and is made into a perfect cube, what would the length of each edge be?

surface area = 9*6 = 54

surface area of cube = 6 s^2
so
6 s^2 = 54
s^2 = 9
s = 3

That will work ok with your piece of plywood since 9 and 6 are both multiples of 3