In a baseball field, the distance from the home plate to the first base is 115 feet. What is the distance from the home plate to the second base? Round to the nearest hundredth.

(1 point)
Responses

230.00 feet
230.00 feet

199.19 feet
199.19 feet

115.00 feet
115.00 feet

162.63 feet

1 answer

In a baseball field, the bases form a square with each side measuring 115 feet. The distance from home plate to second base is the diagonal of this square.

To calculate the diagonal \(d\) of a square, you can use the Pythagorean theorem:

\[ d = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2} \]

where \(a\) is the length of one side. In this case, \(a = 115\) feet.

Now, calculate the distance:

\[ d = 115\sqrt{2} \approx 115 \times 1.41421356 \approx 162.63 \text{ feet} \]

Thus, the distance from home plate to second base is approximately 162.63 feet. So the correct response is:

162.63 feet