SAT Question f89af023: Nonlinear Functions answer and explanation with Desmos solution

Choice A is correct. It's given that the volleyball court is rectangular and has an area of $162$ square meters. The formula for the area of a rectangle is $A=lw$, where $A$ is the area, $l$ is the length, and $w$ is the width of the rectangle. It's also given that the length of the volleyball court is twice the width, thus $l=2w$. Substituting the given value into the formula for the area of a rectangle and using the relationship between length and width for this rectangle yields $162=2w\times w$. This equation can be rewritten as $162=2w^2$. Dividing both sides of this equation by $2$ yields $81=w^2$. Taking the square root of both sides of this equation yields $w=\pm 9$. Since the width of a rectangle is a positive number, the width of the volleyball court is $9$ meters.