In the middle 1800s they did a lot of different experiments. The longest throw on a slow hit ball from 3rd to first was able to beat most runners if the runners had to run more than 30 strides. The disadvantage for 3rd was to field the ball then throw to 1st at rate 3x faster than he can run. They decided on 30 strides. In those days a stride was a yard. So they did it in yards. 30 yards is 90 feet. As the base lines are measured from the center you lose a little in the equation making it a few inches less from center of 3rd to 1st at about 89 feet.
Pitchers used to be able to pitch from anywhere within a 15' area but not from closer than 45'. They finally all agreed in 1850ish to draw the 15' radius mound with its front lip at 45 feet to the plate. And the intersection from plate to second and first to third would be the pitching Cleat or round bit of metal they now call the rubber.
It seemed to work pretty well so they left it that way. The Balk on pitchers was a really contested thing when they made him complete his pitch. You may not know they didn't always call strikes either.
Well somebody asked
