Answer
$88in$
Work Step by Step
We have $l+4b=108$ and the volume $b^2l=2200$
using $l=108-4b$ we have $b^2(108-4b)=2200$
or $4b^3-108b^2+2200=0$ or $b^3-27b^2+550=0$
Solving this equation numerically gives two positive values $b=5, 26.2$, hence
the length of the box is $l=108-4b=88in$ or $3.2in$
We discard the value of 3.2in as it does not fit the definition of the length of the box.