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The wikipedia article on nitric acid mentions the following structure of $\ce{HNO3}$ in which the two $\ce{N-O}$ bonds (other than that of $\ce{N-OH}$) are of different length i.e., $119.9\,\pu{pm}$ and $121.1\,\pu{pm}$.
Structure of Nitric Acid

But it also mentions that $\ce{HNO3}$ molecule is a resonance hybrid of - (only major contributing ones)
enter image description here

I can't understand how can both be simultaneously correct since the resonance hydrid should have same two $\ce{N-O}$ bond lengths (other than $\ce{N-OH}$ one). How is it correct or is the source itself wrong?

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    $\begingroup$ The difference is very minor, such minor differences may be caused by multiple very weak effects rarely significant and consequently rarely discussed and explained. Generally it is expected to have unequal bonds (i.e. not transformed into each other by symmetry transformation) to have slightly different length. Specifically, at least 2 effects may be involved here: 1) effect of charge distribution. Significant polarity of O-H bond makes resonance hybrids unequal in energy, so one has higher impact 2) the unconjugated lone pair of OH oxygen can conjugate with only one another N-O bond. $\endgroup$ – permeakra Apr 16 '16 at 6:56
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In addition to permeakra's comment, I want to add the following thoughts:

1) How were these bond lengths determined?

Were these values determined computationally? If so, what is the standard error in the computational method uses? In other words, is the difference between the two values within the error of the method, and thus the difference is not significant. Additionally, a computational method operates on single molecules "in the gas phase", and there might be just enough interaction between the hydrogen atom and one of the other oxygen atoms. This interaction would also explain the disparity in bond angles:

enter image description here

Were they measured experimentally, for example from x-ray crystallography? If so, then dissymmetry arising from a preferential crystal packing arrangement can lead to differences. In particular, in the solid state, the position of the hydrogen atom can make a big difference in preferential hydrogen bonding, either intermolecularly or intramolecularly. For units like the following hyrogen-bond dimers, the hydrogen bonding could lead to dissymmetry between the N-O bonds.

enter image description here

2) Bonds vibrate

They do, even in the solid state. Thus, an x-ray crystal structure has error its measurements as well. Again, is this difference in bond lengths within the experimental error?

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