The Importance of Margins - Task

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 "Fermat's Last Theorem." 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. This task asks that you design two books, both with a margin area of 300 square centimeters. Book 1: The width of margins on all sides is 3 cm. Book 2:The width of top, bottom, and outer margins is 2 cm. The width of the inner margin is 4 cm
• 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.
The diagram shows different designs with a margin area of 300 square centimeters.