What is the least perimeter of a rectangle with the area of 32 square feet

You get the least perimeter of a rectangle when you draw
a square around the area.

If the area is 32 square feet, then each side of the square
is  √32 feet.   That's  4√2 feet.

So the perimeter (all around all 4 sides) is  16√2 = about  22.6 feet.


There IS a way to get a shorter perimeter around the same area,
but not with a rectangle, or any number of straight sides.

If you do it with a CIRCLE, then the radius of the circle
is about 3.19 feet, and the perimeter (circumference) is
about 20.05 feet ... about 11% shorter than the perimeter
of the square.