Abaseball diamond is a square with sides of 90 feet. what is the shortest distance, to the nearest 10th of a foot, between first base and third-base?

The shortest distance from where to where?
The shortest distance from home plate to second base:
--- From home plate to first base to second base and back to home plate forms a right triangle with the right angle at first base. The distance from home to second is the hypotenuse, so use the Pythagorean Theorem:
c² = a² + b² ---> c² = 90² + 90² ---> c² = 8100 + 8100 ---> c = √16200
---> c ≈ 127.3.