Final answer:
The width of the playground is 35 yards.
Step-by-step explanation:
To find the width of the playground, we can set up an equation based on the given information.
Let's assume the width of the playground is 'w' yards. According to the problem, the length of the playground is 20 yards longer than three times its width.
So, the length would be 3w + 20 yards. The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 320 yards.
Writing an equation based on the perimeter, we can solve for the width:
Perimeter = 2(length + width)
320 = 2((3w + 20) + w)
Now, we can simplify and solve for 'w':
320 = 2(4w + 20)
Dividing both sides by 2:
160 = 4w + 20
Subtracting 20 from both sides:
140 = 4w
Dividing by 4:
w = 35
Therefore, the width of the playground is 35 yards.