What is a good size artificial synthetic putting green for my backyard? How about turf height?

I am taking out a 27′ round pool and putting in a putting green. There is a dealer with a section that is 3/4 high 13’x15′. Or another dealer with a section of 1 1/4 high 12×24′. Which of these would be better? Is the 1 1/4 grass too tall for a putting green, even with infill? Thanks so much!

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