Question

baseball diamond a baseball diamond is a square that is 90 feet on each side. how far is it from home plate to second base? round to the nearest hundredth. second base 127.28 feet home plate 90.50 feet 107.28 feet 97.50 feet

Explanation:

Step1: Apply the Pythagorean theorem

The distance from home plate to second base is the diagonal of a square with side length \(a = 90\) feet. For a right - triangle (half of the square) with legs \(a = 90\) and \(b=90\), by the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (the diagonal of the square). So \(c^{2}=90^{2}+90^{2}\).

Step2: Calculate \(c^{2}\)

\(90^{2}+90^{2}=8100 + 8100=16200\). Then \(c=\sqrt{16200}\).

Step3: Simplify \(\sqrt{16200}\)

\(\sqrt{16200}=\sqrt{8100\times2}=90\sqrt{2}\approx90\times1.4142 = 127.28\)

Answer:

127.28 feet