#### Answer

length: $9$, width: $6$

#### Work Step by Step

Put the information given into formulas. Solve for the width by using the values for length and width in the area formula, and then factor. Only the positive value matters since you cannot have a negative width on a shape.
Next, plug in the width to the length formula to find the length.
$L=w+3$
$A=Lw=54$
$A=Lw$
$(w+3)(w)=54$
$w^2+3w-54=0$
$(w+9)(w-6)=0$
$w=-9,6$
$w=6$
$L=6+3$
$L=9$