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

The maximum length of the playground is 38 meters, given that the perimeter cannot exceed 120 meters and the width cannot exceed 22 meters. The possible lengths are therefore from 0 to 38 meters.

Step-by-step explanation:

Possible Lengths of the Playground

• The problem states that the perimeter of a rectangular playground can be no greater than 120 meters, with a maximum width of 22 meters.
• The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.
• We can rearrange this formula to solve for the length (l): l = (P/2) - w.

Given that the maximum width (w) is 22 meters and the maximum perimeter is 120 meters, we can substitute these values to find the maximum length:

• l = (120/2) - 22

• l = 60 - 22

• l = 38 meters

The maximum length of the playground is 38 meters. However, the length can be any value less than or equal to 38 meters, so the possible lengths of the playground are from 0 meters to 38 meters.

Answer 2

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.