To find the new width of the photograph when it is enlarged by a factor of 4.5, you can multiply the original width by the enlargement factor.
The original width is 5.5 inches.
Calculating the new width:
\[ \text{New Width} = \text{Original Width} \times \text{Enlargement Factor} = 5.5 \times 4.5 \]
Now, performing the multiplication:
\[ 5.5 \times 4.5 = 24.75 \]
Thus, the new width of the photograph is
\[ \boxed{24.75} \text{ inches.} \]