Question

a baseball field is in the shape of a square. the distance between each pair of bases along the edge of the square is 90 feet. what is the distance between home plate and second base?
√2 feet

Explanation:

Step1: Apply Pythagorean theorem

In a square with side - length \(a = 90\) ft, for the diagonal \(d\) (distance from home plate to second base), if the right - triangle has legs of length \(a\) and \(a\), by \(d^{2}=a^{2}+a^{2}\).

Step2: Substitute \(a = 90\)

\(d^{2}=90^{2}+90^{2}=8100 + 8100=16200\).

Step3: Solve for \(d\)

\(d=\sqrt{16200}=90\sqrt{2}\text{ ft}\)

Answer:

\(90\sqrt{2}\text{ ft}\)