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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)

 c^{2} = a ^{2} + a ^{2}
 c^{2} = 2(a ^{2} )

c ^{2} = 2(90) ^{2}
 \sqrt{c ^{2} } = \sqrt{2(90) ^{2} }
c = 90 \sqrt{2} feet

The distance from the home plate to second base is 90 \sqrt{2}  feet
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