Questions: A baseball diamond is in the shape of a square with 80 ft sides. How far is it from home plate to second base? Give the exact value. Write the answer in simplest form. Then give an approximation to the nearest tenth of a foot.

A baseball diamond is in the shape of a square with 80 ft sides. How far is it from home plate to second base? Give the exact value. Write the answer in simplest form. Then give an approximation to the nearest tenth of a foot.

Transcript text: A baseball diamond is in the shape of a square with 80 ft sides. How far is it from home plate to second base? Give the exact value. Write the answer in simplest form. Then give an approximation to the nearest tenth of a foot.

Solution

Solution Steps

Step 1: Understand the Problem

The problem involves finding the distance from home plate to second base on a baseball diamond, which is a square with each side measuring 90 feet.

Step 2: Identify the Relevant Formula

To find the distance from home plate to second base, we need to calculate the diagonal of the square. The formula for the diagonal \(d\) of a square with side length \(s\) is: \[ d = s\sqrt{2} \]

Step 3: Substitute the Given Values

Given that the side length \(s\) is 90 feet, substitute this value into the formula: \[ d = 90\sqrt{2} \]

Step 4: Simplify the Expression

The exact value of the distance from home plate to second base is: \[ d = 90\sqrt{2} \text{ feet} \]

Step 5: Approximate the Distance

To approximate the distance to the nearest tenth of a foot, calculate the numerical value of \(90\sqrt{2}\): \[ 90\sqrt{2} \approx 90 \times 1.414 \approx 127.3 \text{ feet} \]