The perimeter of a rectangular playground can be no greater than 120 meters. The width of the playground cannot exceed 22 meters. What are the possie lengths of the playground?

There are an infinite number of values satisfying the requirements; every couple of numbers satisfying the following conditions are valid:

base = 60-w meters

width = w meters

0 < w < = 22

Step-by-step explanation:

Since the playground has a rectangular shape, let us us call b the base of the rectangle and w its width. In order for the rectangle to satisfy the condition of P = 120, we need for the following equation to satisfy:

2b + 2w = 120

Solving for b, we get that b = (120 - 2w) / 2 = 60 - w.

Given a particular value (w) for the width, the base has to be: (60-w).

Therefore, the possible lengths of the playground are (60-w, w), where 60-w corresponds to the base of the rectangle and w to its width. And w can take any real value from 0 to 22.