Answer:
The length of the diagonal of the playground is approximately 42.42 yards.
Step-by-step explanation:
As the playground is square we know the formula for its perimeter: \(P=4l\), where \(l\) stands for the length of the side of the playground. By the statement of the problem we know that \(P=4l=120 yd\), then it is not difficult to find that \(l=30\) yards.
If we trace the diagonal we see that a right triangle is formed, where the diagonal is its hypotenuse, and its sides are the sides of the playground. Then, using Pythagoras theorem (we denote by \(d\) the length of the diagonal), we have
\(d = \sqrt{30^2+30^2} = \sqrt{1800}\approx 42.42\).
Thus, the diagonal has (approximately) 42.42 yards.
