The design with the least perimeter would be a 6 x 6 SQUARE. The perimeter would be 6+6+6+6 = 24
As you increase the length and reduce the width, the perimeter increase. For example, a 9 x 4 rectangle would have a perimeter of 9+9+4+4 = 26. Until you achieve the maximum perimeter with the longest length and shortest width which is a 36 x 1 RECTANGLE.
The design with the greatest perimeter would be a 36 x 1 RECTANGLE.
In general, the whole number rectangle that has the greatest perimeter has a WIDTH OF ONE and a length equal to the area.
The rectangle with the least perimeter has equal length and width, which is a SQUARE.