Carpetting a Rectangular Room

You have 36 square feet to carpet a room in your house. The drywall that you are using for the walls are expensive, so you want the perimeter of the room to be as small as possible. Use centimeter tiles to investigate. Each tile represents one square foot of carpet.

If the room had to be rectangular, what arrangements of rooms could you have? Sketch the rooms and calculate the area and perimeter.

What dimensions of rectangular rooms has the largest perimeter?

What dimensions of rectangular rooms has the smallest perimeter?

If you were calling a friend to describe the room with the smallest perimeter, write a description of what you would say.

Possible Extensions:
Based on the investigation above, what would be the dimensions of a room that had the smallest perimeter and an area of 100 square feet. Explain your answer.