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

Step2: Simplify the equation

Substitute \(a = 90\) into \(d^{2}=a^{2}+a^{2}\), we get \(d^{2}=90^{2}+90^{2}=2\times90^{2}\). Then \(d = 90\sqrt{2}\) feet.

Answer:

\(90\)