Problem

Source: Cono Sur 2009 #6

Tags: geometry, combinatorial geometry, cono sur, rectangle



Sebastian has a certain number of rectangles with areas that sum up to 3 and with side lengths all less than or equal to $1$. Demonstrate that with each of these rectangles it is possible to cover a square with side $1$ in such a way that the sides of the rectangles are parallel to the sides of the square. Note: The rectangles can overlap and they can protrude over the sides of the square.