Area = 38 1/4 = 153/4
Width = 4 1/2 = 9/2
Area = Length x Width
Length = Area/Width
So divide both of them:
[tex]\sf{ \frac{153}{4} \div \frac{9}{2} =\sf{ \frac{153}{4} \times \frac{2}{9} = \frac{9 \times 17}{2\times 2}\times \frac{2}{9} = \frac{17}{2}[/tex]
So the length is equal to [tex]\boxed{\sf{\frac{17}{2}}}[/tex]
