A baseball 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.