The width is 30 meters and the area is 1800 square meters.
Your question doesn't seem complete. If you're trying to find the width of the playground (how wide) then imagine a rectangle, the opposite sides are equal in length and all the angles are right angles( 90 degrees).
Since the perimeter is 180 meters
180 = 60 + 60 + w +w (let w stand for width)
180=120 + 2w
60 = 2w
Finding the area
A = 1800