Occasionally, the book's margins can be more important than the book itself. The mathematician Fermat used the margins of one of his books to scribble a mathematical result known today as "[url=http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem]Fermat's Last Theorem.[/url]" He added the he had found a wonderful proof for that result, but that there was not enough room in the margins to describe it.[br]This task asks that you design two books, both with a margin area of 300 square centimeters. [b][br][/b]Book 1: The width of margins on all sides is 3 cm.[br]Book 2[b]:[/b]The width of top, bottom, and outer margins is 2 cm. The width of the inner margin is 4 cm[br][list][*]For each book describe the different design options that satisfy all requirements.[/*][*]For each book find a design that makes the text area as large as possible.[/*][*]Generalize the investigation to the case of any given margin area and any given margin widths. Find general expressions for page height and width that maximize the text area.[br] [/*][/list]The diagram shows different designs with a margin area of 300 square centimeters.