The area of a baseball field bounded by home plate, first base, second base, and third base is a square. if a player at first base throws the ball to a player at third base, what is the distance the player has to throw?

Well the question doesnt show any number for a side or anything but we can solve this with algebra if we say that a side from one base to next has a length of x. so we know each side has length x and that the shape they make is square. This means we are only searching for the diagonal of a square.

remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using the pythagoream theorem we can say that
a^2 + b^2 = c^2

we said all side lengths are x so we can put x in for a and b and get

x^2 + x^2 = c^2

2x^2 = c^2

c = x * squareroot(2)

that is the basic fundamental answer that will always work when working with diagonals of squares.

so if the length between bases is 90 ft, we could plug this in and get
c = 90 ft * squareroot(2)
c = 127.28 ft