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Advanced Math / Nonlinear functions Difficulty: Medium

A rectangle has a length that is $15$ times its width. The function $y equals left parenthesis 15 w right parenthesis left parenthesis w right parenthesis$ represents this situation, where $y$ is the area, in square feet, of the rectangle and $y greater than 0$ . Which of the following is the best interpretation of $15 w$ in this context?

The length of the rectangle, in feet

The area of the rectangle, in square feet

The difference between the length and the width of the rectangle, in feet

The width of the rectangle, in feet

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Explanation

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 $y equals left parenthesis 15 w right parenthesis left parenthesis w right parenthesis$ represents this situation, where $y$ is the area, in square feet, of the rectangle and $y greater than 0$ . 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 $15 w$ represents the length of the rectangle, in feet. Therefore, the best interpretation of $15 w$ 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 $15 w$ , 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 $15 w$ , in the given function.