I think you have to enlarge the same percentage in both directions.
It looks like the original pattern uses 2.5 inch strips and 1.5 inch strips, so 2 inch and 1 inch finished. So each of the 4 large squares has 11 2-inch strips and 12 1-inch strips, for a total of 34 inches. The length and width of the quilt is then 2*34 (two large blocks) + 3*2 (2 borders and middle sashing), which comes to 76
if you make them finish at 3 and 1.5 (that is, make them 50% larger), the squares will be 33+18=51 inches, and the quilt will end up at 2*51 + 3*3 = 111 . That'd give you about 15" overhang on a king if it's 80" wide.
For lengths, just as an example: If the original pattern piece is 2.5 by 10.5, your enlarged version would be 3.5 by 15.5 (I think): you'd make the 50% percentage adjustment to the finished size of the piece, so 2 by 10 becomes 3 by 15 in this example, and then add the seam allowance back in, to get 3.5 by 15.5
Does that make sense? I've never done this, but it seems like a valid approach.