For trapezoid there exists the well-known formula

EF = 1/2 ( AB + DC ) which is normally given by

m= (a+b)/2, where a and b are the parallel sides and m is the length of the median.

By that formula we have:

12 = EF = (AB+DC)/2 = ( x-5 + 2x -1 ) /2 = (3x -6) / 2

=> x=10

and so we have:

AB = x-5 = 10-5 = 5

As you can see it is not required to have the length of AD and BC if you want to determine the length of AB. These both values however could be used to calculate the diagonals of the trapezoid, which are √340 and √244