Question

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?

Answer 1

Answer:

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.