To arrange the carpet squares to have the smallest perimeter, Mrs. Smith should arrange them in a square shape. This means that she should arrange the carpet squares into a rectangle with equal length and width. If she has 42 carpet squares, she could arrange them into a rectangle that measures 6 squares by 7 squares. This would give her a total perimeter of 26 squares (6+6+7+7), which is the smallest possible perimeter for 42 squares arranged in a rectangular shape.
