Answer
1.5 inches
Work Step by Step
We call the length shaded off x. Recall, since it is shaded off both sides and both ends, a total of 2x is cut off of each side and end. Thus:
$ 165 = (18 -2x)(14-2x ) \\ 165 = 4x^2 -64x + 252 \\ 0 = 4x^2 -64x + 87 \\ (2x-29)(2x-3) $
Since there would be a negative width if 14.5 inches were shaded off, we obtain that the amount shaded is x=1.5 inches.
