Answer
The width of the sign is 6 feet, and the length is 9 feet.
Work Step by Step
With $ w $ being the width of the sign, its length is $ w+3$
Area = (width)$\times $(length)
$54=w(w+3)$
$54=w^{2}+3w $
$0=w^{2}+3w-54$
Factor the RHS by finding factors of -54 with sum +3
We find $+9$ and $-6$
$0=(w+9)(w-6)$
$ w=-9$ is discarded as a negative width, which makes no sense.
$ w=6$ (feet) is the width of the sign.
The width of the sign is 6 feet, and the length is 9 feet.
