I'd also like to see the pattern in question. I'm not big on square quilts myself but the way I make them rectangular varies. Easiest but not always effective is to double the width of the borders on the top and bottom from what is on the sides, that turns a square into a crib sized pretty easily but maybe not so good on bigger/wider quilts.
Another trick I use pretty often is to take a sub unit of the block and turn it on point, basically that makes it about 1.5 times as wide as block straight set. I'll put those to the top and bottom of the square. You can put a frame of a coordinating fabric around your square to whatever measurement you need for the width. I used to be good at math but I have a heck of a time post-50 so I just make the units and connect them and figure out the width from there...
Likewise, when the square isn't as big as you want it, turning it on point and putting corners on all four sides quickly makes it much bigger and shows off the center square (now a medallion!). Then you can put on the additional borders/widths.