Summary: Selecting the “better” solution to a problem between the first one that comes to mind and the alternative that may follow is not a {\it fait-accompli}. After all, is it better if it is more economical? Or is it better if it is more elegant? Moreover, taking shortcuts does not always lead to a shorter solution. Consider the simple example of a rectangle modified so as to preserve its area. In this article, the authors put forward two methods for investigating this simple example. The first method that links a rectangle to another with the same area, and to a square of the same area. The second method links the two rectangles directly by way of what the authors refer to as “mathematical elegance”. The authors conclude by outlining the parameters associated with the constructions, as well as comparing the space required for the implementation of these different pathways, in order to make the selection process a little easier. (ERIC)