1. The problem statement, all variables and given/known data (11) a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square. b) Show that of all the rectangles with a given perimeter, the one with greatest area is a square. 2. Relevant equations - Differentiation rules - Superhuman powers 3. The attempt at a solution I'm completely lost on this one. I honestly don't even know where to start. Of all the rectangles with a given area? What? So let's introduce some variables. Say we have 3 rectangles. Their areas are a1, a2, a3. Then their perimeters are p1, p2, p3. Now if p2 > p1 <p3, i.e. p1 is the smallest of the three perimeters, then the rectangle 1, with area a1 and perimeter p1 is square. I get the question.. but I still don't have a clue about where or how to start. Since b) is very similar, the same goes for b).