For which molecule is the external double bond shorter? 1-[(1E)-1-butenyl]-4-nitrobenzene or butenylbenzene ?
I think the longer bond length will be in case of first one.
The presence of nitro gr in the second one is in conjugation with the lone pair at the end of red bond will give red bond more double bond character by resonance effect due to withdrawal of electron . So its red bond length will be shorter.
The non-nitro molecule has the longer bond.
If you draw resonance structures for both compounds, you would get that the carbon immediately adjacent to the negatively-charged carbon is more electropositive for the nitro compound, i.e. it is more electron-deficient at that carbon.
To maintain the stability of the bond, having lost some electron density, it wants to maintain its optimal electron distribution, so it pulls the electron density from the nearest,
It's like disturbing an electron distribution "equilibrium" by grabbing electrons away from the "products" side (the slightly positive carbon); more electrons "flow" from the "reactants" side (the anionic carbon) to "reequilibrate". But since the average distance of these electrons is now closer, the bond is now shorter.
Therefore, since the nitro group evidently draws electrons in more strongly than a hydrogen does, the bond on the compound with no nitro group is longer.