What is the maximum area?

Question

132 meters of fencing with which to make 2 side by side rectangular enclosures against existing wall. If the rectangular enclosures are adjacent and of the same depth, what is the maximum area that can be enclosed?

Answer 1

You should start by drawing a picture.

 

You know the total area is equal to depth * width. (width being the combine width of both rectangles.) You also know the perimeter, 132 = 3 * depth + width. This gives you an equation: area = depth * (132 - 3 * depth). Now find the maximum value for the variable area in terms of depth. (This can be done different ways depending on what class you are in.)