This puzzle is based on problem 11057 from the American Mathematical Monthly (January 2004): Given three lengths x, y, and z, what is the largest possible area of a rectangle ABCD if there is a point P inside the rectangle for which AP=x, BP=y, and CP=z?

In this applet, the point P is at the center, and the other points are allowed to move, but are constrained to the first, second, and third quadrants. (That is, A needs to be between 12 o'clock and 3 o'clock, B is between 9 and 12, and C is between 6 and 9.)

Click and drag points to change the angle and length of the "sticks." You can also change the length by entering a number and then clicking "x", "y", or "z". Lock the stick lengths to allow only the angles to change. Try to achieve the maximum area for a given set of stick lengths.

(If you do not see the buttons and checkboxes in the applet, try reloading this page.)