Question

a baseball diamond is a square with sides of 90 feet. what is the shortest distance, to the nearest tenth of a foot, between first base and third base?

Explanation:

Step1: Identify the shape and formula

The baseball diamond is a square, so the distance between first base and third base is the length of the diagonal of the square. The formula for the diagonal \(d\) of a square with side length \(s\) is \(d = s\sqrt{2}\).

Step2: Substitute the side length

Given \(s = 90\) feet, substitute into the formula: \(d = 90\sqrt{2}\).

Step3: Calculate the value

\(\sqrt{2}\approx1.4142\), so \(d = 90\times1.4142 = 127.278\).

Step4: Round to the nearest tenth

Rounding \(127.278\) to the nearest tenth gives \(127.3\).

Answer:

127.3 feet