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The image contains a problem about a baseball diamond, which is shaped like a square. The distance from home plate to second base is given as \(127 \frac{1}{2}\) feet, and you need to find the distance between the bases.

Since a baseball diamond is a square, the distance from home plate to second base is the length of the diagonal of the square. Let \(s\) be the length of a side of the square (the distance between any two bases). The relationship between the diagonal \(d\) and the side length \(s\) of a square is given by the Pythagorean theorem:
\[
d = s\sqrt{2}
\]

Given \(d = 127.5\) feet, we can solve for \(s\) as follows:
\[
s = \frac{d}{\sqrt{2}} = \frac{127.5}{\sqrt{2}}
\]

Let's calculate this to find the side length \(s\), rounded to the nearest whole number.The distance between the bases on the baseball diamond is approximately **90 feet**.

Would you like to explore further details or have any questions on this topic?

Here are some related questions you might consider:
1. How would the answer change if the baseball diamond were not a perfect square?
2. What is the area of the baseball diamond?
3. Can you explain how the Pythagorean theorem applies to other sports field dimensions?
4. How does the rounding of the diagonal distance affect the accuracy of the side length?
5. What are some real-world applications of the Pythagorean theorem besides sports?

**Tip:** Always double-check unit conversions and rounding rules when calculating measurements for sports fields, as precision can impact game rules and play.

A baseball diamond has the shape of a square in which the distance from home plate to second base is approximately 127 1/2 feet. Approximate the distance between the bases. (Round your answer to the nearest whole number.)

Learn how to calculate the distance between the bases on a baseball diamond. Given the diagonal distance from home plate to second base is 127 1/2 feet, use the Pythagorean theorem to find the approximate side length. The solution is detailed step-by-step with key geometric formulas, suitable for students in Grades 8-10.

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