Answer
$B$ and $C$.
Work Step by Step
$A$
$2x+2(x-1)=14$
$2x+2x-2=14$
$4x-2=14$
$4x=16$
$ x=4\qquad$ ... can be a side length of a rectangle.
$B$
$-2x+7(5-x)=52$
$-2x+35-7x=52$
$-9x+35=52$
$-9x=17$
$ x=-\displaystyle \frac{17}{9}\qquad$ ... can not be a side length of a rectangle (negative length).
$C$
$5(x+2)+5x=10$
$5x+10+5x=10$
$10x+10=10$
$10x=0$
$ x=0\qquad$ ... can not be a side length of a rectangle (zero length).
$D$
$2x+2(x-3)=22$
$2x+2x-6=22$
$4x-6=22$
$4x=16$
$ x=4\qquad$ ... can be a side length of a rectangle.