365 factorises: 5*73. So you could make a rectangle 5 by 73 squares but the blanket is 90 by 102.
The nearest square to 365 is 361, which is 19 squared. That leaves you with four squares over if you make a square of 19 by 19. You could use the 4 odd ones as an extra square next to the 10th square on each side:
The size of the squares would be based on a 21 by 21 square pattern so the size would be 90/21=30/7 or smaller to fit the shorter side of the blanket. I suspect the units are inches. So that would be 4.29". To allow for a border 4.25" might be better and easier to measure. You would end up with a square side 89.25" allowing for the protuberances. The main square would have a side of 80.75", but the four odd squares would give you an extra 8.5" on each side making up to 89.25".