College Math Placement Practice Test 2026 – Comprehensive All-in-One Guide for Exam Success!

To find the length of the diagonal of a square playground with a given perimeter, we first need to determine the side length of the square. The perimeter of a square is calculated using the formula:

\[ \text{Perimeter} = 4 \times \text{side length} \]

Given the perimeter of the square is 120 yards, we can set up the equation:

\[ 120 = 4 \times \text{side length} \]

To find the side length, we divide both sides by 4:

\[ \text{side length} = \frac{120}{4} = 30 \text{ yards} \]

Next, we use the relationship between the side length and the diagonal of a square. The diagonal \(d\) of a square can be calculated using the formula:

\[ d = \text{side length} \times \sqrt{2} \]

Substituting the side length we found:

\[ d = 30 \times \sqrt{2} \]

Thus, the length of the diagonal is:

\[ d = 30\sqrt{2} \text{ yards} \]

This means the correct answer is that the length of the diagonal is 30√2 yards