Question

second base third base first base 90 ft home plate 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? \boxed{} \sqrt{2} feet

Explanation:

Step1: Identify the triangle type

The baseball field is a square, so the triangle formed by home plate, first base, and second base is a right - triangle with legs of length 90 feet (since the distance between consecutive bases is 90 feet) and we need to find the hypotenuse (distance between home plate and second base).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 90\) and \(b=90\). So \(c=\sqrt{90^{2}+90^{2}}=\sqrt{8100 + 8100}=\sqrt{16200}\). We can simplify \(\sqrt{16200}\) as follows: \(16200=8100\times2\), so \(\sqrt{16200}=\sqrt{8100\times2}=90\sqrt{2}\).

Answer:

\(90\)