The length of a rectangle is 50 inches and the width is x inches. The perimeter

Choice A is correct. The perimeter of a rectangle is equal to the sum of $2$ times its length and $2$ times its width. It's given that the rectangle's length is $50$ inches and the width is $x$ inches. Therefore, the perimeter, in inches, is $2\left(50\right)+2x$, or $100+2x$, which is equivalent to $2x+100$. It's given that the perimeter is at most $210$ inches; therefore, $2x+100\le 210$ represents this situation.

Choice B is incorrect. This inequality represents a situation where the perimeter is at least, rather than at most, $210$ inches.

Choice C is incorrect. This inequality represents a situation where $2$ times the length, rather than the length, is $50$ inches.

Choice D is incorrect. This inequality represents a situation where $2$ times the length, rather than the length, is $50$ inches, and the perimeter is at least, rather than at most, $210$ inches.