An area rug has an area of 48 square feet. two similar rugs have areas of 108 square feet and 192 square feet. in each rug, the length is 1 1/3 times the width. which of the following could be the dimensions of one of the area rugs?

For area A, the width will be √(3A/4), so for the three rugs, the widths are 6 ft, 9 ft, 12 ft. Corresponding lengths are 4/3 times that, so are 8 ft, 12 ft, 16 ft.

The rug dimensions are
.. 6 ft x 8 ft
.. 9 ft x 12 ft
.. 12 ft x 16 ft

Pick the one(s) that are on your list.