Answer
$\approx84.85\text{ ft}$ (to 2 d.p.).
Work Step by Step
As seen in the diagram below, connecting the bases/home plate forms a square of area $3600 ft^{2}$. Since this is a square, all interior angles are $90°$
The area of a square is given by:
$A=s^2$
Where $s$ is the side length of the square. We use this to find the side length of the square (i.e, the distance between adjacent bases/plates):
$A=s^2$
$3600=s^2$
$s=±\sqrt{3600}$
$s=±60 ft$
However, since a length cannot be negative, we disregard the negative solution. Therefore the side length of the square is $60ft$.
To find out how far a throw is from second base to home plate, we draw a line from second base to home plate, forming a right triangle. The distance from the second base to home plate is the hypotenuse of this triangle, with the other two sides of the triangles being the sides of the square which we previously worked out.
Therefore, using:
$a^2 + b^2=c^2$,
Where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse, we get:
$60^2 + 60^2=c^2$
$c^2=7200$
$c=\sqrt {7200}$
$\approx84.85 ft$ (to 2 d.p.).
