Since the playground has a square shape, its perimeter is given by four times its side length, so:
[tex]\begin{gathered} \text{Perimeter}=4\cdot\text{side} \\ 120=4\cdot\text{side} \\ \text{side}=\frac{120}{4}=30\text{ yards} \end{gathered}[/tex]
Then, to find the length of a diagonal, we can use the formula below:
[tex]\begin{gathered} \text{diagonal}=\text{side}\cdot\sqrt[]{2} \\ \text{diagonal}=30\sqrt[]{2\text{ yd}} \end{gathered}[/tex]
Therefore the correct option is the second one.
