Length is 12ft, width is 4 ft.
2 x (length + width) = perimeter = 32 ft
⇒ length = 16ft - width [1]
length x width = area = 48 sq ft
Using [1] above:
⇒ (16ft - width) x width = 48 sq ft
multiplying out and rearranging:
⇒ width2 - 16 x width + 48 = 0
factorizing:
⇒ (width - 4)x(width - 12) = 0
Thus width = 4 or 12, so using [1] above:
⇒ width = 4ft, length = 16 - 4 = 12ft
or width = 12ft, length = 16 - 12 = 4ft
Convention is that the length is larger than the width, thus rectangle is 12ft long by 4 ft wide.
