College Math Placement Practice Test 2025 - Free College Math Questions and Study Guide

To find the distance of the diagonal in a square, you can use the formula derived from the Pythagorean theorem. For a square with side length \(s\), the diagonal \(d\) can be calculated using the formula:

\[

d = s\sqrt{2}

\]

In this case, the side length is given as 30 yards. By substituting this value into the formula, the calculation becomes:

\[

d = 30\sqrt{2}

\]

This result represents the length of the diagonal in yards. The value \( \sqrt{2} \) is approximately 1.414, making the diagonal longer than the length of the sides but still containing the factor of the side length.

Thus, when you calculate the diagonal for a square with a side length of 30 yards, the diagonal is indeed:

\[

30\sqrt{2} \text{ yards}

\]

This aligns perfectly with the answer provided, confirming its accuracy through the geometric properties of squares.