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Ans is option (A)

Using the cosine rule of triangle trigonometry ,

$cosC=\frac{a^{2}+b^{2}-c^{2}}{2ab}$

$\Rightarrow$   $cos120^{\circ}=\frac{64+144-c^{2}}{2\times8\times12}$

$\Rightarrow$  $c^{2}=304$   $\Rightarrow$  $c=4\sqrt{19}km$
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