设 $x,y\in R$向量 $\stackrel{\rightharpoonup }{a}=(x,1),\stackrel{\rightharpoonup }{b}=(1,y),\stackrel{\rightharpoonup }{c}=(2,-4)$，且 $\stackrel{\rightharpoonup }{a}\perp \stackrel{\rightharpoonup }{c},\stackrel{\rightharpoonup }{b}//\stackrel{\rightharpoonup }{c}$，则 $\left|\stackrel{\rightharpoonup }{a}+\stackrel{\rightharpoonup }{b}\right|=$（）

A．

$\sqrt{5}$

B．

$\sqrt{10}$

C．

$2\sqrt{5}$

D．

10