Hello, epetrik!

The perimeter of a rectangle is to be between 170 and 230 inches.

Find the range of values for its length when its width is 45 inches.

We know that: .

Since , we have: .

The perimeter is between 170 and 230 inches.

. .

Therefore, the length must be between 40 and 70 inches.

The perimeter of a square is to be from 45 meters to 90 meters.

Find the range of values for its area.

Let = side of the square.

The perimeter of a square is: .

The perimeter is between 45 and 90: .

Divide by 4: .

The length of the side is between 11¼ and 22½ meters.

The area of the square is: .

So we have: .

Therefore: .

The area is between: .