sat-dog

Choice A is correct. It's given that a rectangle has a length that is $15$ times its width. It's also given that the function $y=\left(15w\right)\left(w\right)$ represents this situation, where $y$ is the area, in square feet, of the rectangle and $y>0$. The area of a rectangle can be calculated by multiplying the rectangle's length by its width. Since the rectangle has a length that is $15$ times its width, it follows that $w$ represents the width of the rectangle, in feet, and $15w$ represents the length of the rectangle, in feet. Therefore, the best interpretation of $15w$ in this context is that it's the length of the rectangle, in feet.

Choice B is incorrect. This is the best interpretation of $y$, not $15w$, in the given function.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect. This is the best interpretation of $w$, not $15w$, in the given function.