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: [tex]P=4l[/tex], where [tex]l[/tex] stands for the length of the side of the playground. By the statement of the problem we know that [tex]P=4l=120 yd[/tex], then it is not difficult to find that [tex]l=30 [/tex] 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 [tex]d[/tex] the length of the diagonal), we have
[tex]d = \sqrt{30^2+30^2} = \sqrt{1800}\approx 42.42[/tex].
Thus, the diagonal has (approximately) 42.42 yards.
