Let x = width and y = length.
xy = 384
2x + 2y = 80
solve the system of equations:
x = 384/y
2(384/y) + 2y = 80
384/y + y = 40
384 + y^2 = 40y
y^2 - 40y + 384 = 0
(y - 16)(y - 24) = 0
y - 16 = 0 or y - 24 = 0
y = 16 or y = 24
x = 24 or x = 16
The dimensions of the room are 16ft and 24ft.