Suppose you consider a rectangular floor space of 36 square meters with a whole-number side lengths. Which design has the least perimeter? Which has the greatest perimeter? Explain your reasoning.

In general, describe the rectangle with whole-number dimensions that has the greatest perimeter for a fixed areal. Which rectangle has the least perimeter for a fixed area?

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.