Are you going to miter them at the corner? Otherwise your won't have a continuous border of each fabric. You will have a striped effect at the corners.
That being said, if you still intend to do what I understand you to say I would sew the individual fabrics the the proper length and join them to the others. I would also stagger the seams so that you don't have them sort of matching but not quite.
Clear as mud, right?