The bad thing is that your new measurements don't fall on a nice even fraction. The way I read your dilemma is that you need to sew 3 smaller squares together and they need to add up to 11.5"
The math gets a little hairy but here is what I would do:
Cut the strips at 2 3/8" (you can either cut them skinny or make a wider seam allowance)
Sew them together to where your block is approximately 4 3/16"
3 blocks at 4 3/16" will get you to 11.5" blocks. You may need to fiddle with the seam allowance a tiny bit.
If you want to understand the math:
It will take a total of 1" seam allowance by the time you sew the 3 squares together, so 11.5" plus 1" = 12.5"
Divide 3 into 12.5" = 4.17" that is the size of each square. Looking at the decimal equivalency chart, .17 falls close to 3/16" so I would make my squares 4 3/16" square and adjust the seam allowance to match to the big square.
Now how to get to the 4 3/16" square.
If it is made by sewing 2 strips together, then it will need a 1/2" seam allowance 4.18 plus .5 = 4.68 Divided by 2 = 2.34" (The width of each stripe) That is an even wonkier number on the decimal list so I would cut the strips a skinny 2 3/8"