Final answer:
The maximum area of a rectangle inscribed within another rectangle with length l and width w is the area of the outer rectangle itself, which is lw (Option A).
Step-by-step explanation:
The question is asking to determine the maximum area that a rectangle can have when it is inscribed within another rectangle with known dimensions. To inscribe one rectangle within another means to fit it entirely inside the given rectangle, and the inscribed rectangle can share one or more edges with the bigger rectangle.
The maximum area of an inscribed rectangle will be achieved when it shares all the edges with the given rectangle - essentially when it is the same size as the outer rectangle. Therefore, the maximum area of the inscribed rectangle within another rectangle of length l and width w is simply the area of the outer rectangle itself, which is calculated by the formula Area = length × width, or A = lw.
The correct answer is Option A: lw.