Are you quilting or sending to quilter? For 'most' LAQ's you will want it approx 8 inches larger, both directions. So for your 48 inch square quilt you will need it to be approx 56 inches back. That means you will only need approx 12 inches more. If it was me, I would go for the 56 length first, which is 1.5 yards. Now if you want the back to be all the same fabric, then you would need a total of 3 yards.
Next options ~ do you have left overs from piecing the front? You could piece something to make up the 12+ inches. I have split the my 44" down the middle and put other fabric in the middle, so I have 3 sections in the back. Also I usually take a 1/2" seams for my back piecing.