Maximum Area if Fixed Perimeter

If a rectangle has a fixed perimeter, find for what dimensions the rectangle will have maximum area.
  • Change the shape of the rectangle by moving the blue point.
  • The red point in the first quadrant has x-coordinate equal to one side of the rectangle and y-coordinate equal to the area of the rectangle. Observe the way the point is moving to find when the rectangle will have maximum area.
  • Show the locus of the point.
  • Find the function that will describe the area as a function of one side of the rectangle and enter it in the input box. Hit Enter to graph it.