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?
\\( \sqrt { 2 } \\) feet

Explanation:

Step1: Apply Pythagorean theorem

Let the side of the square \(a = 90\) feet. The distance \(d\) between home - plate and second base is the length of the diagonal of the square. For a right - triangle (half of the square) with legs \(a\) and \(a\), by the Pythagorean theorem \(d^{2}=a^{2}+a^{2}\).
Substitute \(a = 90\): \(d^{2}=90^{2}+90^{2}=8100 + 8100=16200\).

Step2: Simplify the expression

Factor out \(900\) from \(16200\): \(d^{2}=900\times18\). Then \(d=\sqrt{900\times18}=\sqrt{900}\times\sqrt{18}=30\times3\sqrt{2}=90\sqrt{2}\).

Answer:

\(90\)