The distance from home plate to second base is the diagonal of the square.
The diagonal of the square is also the hypotenuse of the right triangles formed when a diagonal is drawn from one vertex to the opposite vertex.
Using the Pythagorean Theorem:
Let diagonal be c, and the side be a (since the baseball diamond is a square, hence, all sides are equal)
[tex] c^{2} = a ^{2} + a ^{2} [/tex]
or
[tex] c^{2} = 2(a ^{2} )[/tex]
[tex]c ^{2} = 2(90) ^{2} [/tex]
[tex] \sqrt{c ^{2} } = \sqrt{2(90) ^{2} } [/tex]
[tex]c = 90 \sqrt{2} feet[/tex]
The distance from the home plate to second base is [tex]90 \sqrt{2} feet[/tex]
