A letter F is composed of 6 unit squares and two rectangles of unit width as in the figure:

Find the lengths of the two rectangles such that the center of gravity is at the center of the middle square.

The big F below is a generalization of the original F. Rectangles A and B are 1 by 1 squares. Rectangles C and D are 1 by x. Rectangle E is 1 by y. Rectangle F is 1 by z.

+----------------+

| A| E |

+--+-------------+

| |

| C|

| |

+--+-----+

| B| D |

+--+-----+

| |

| |

| |

| F|

| |

| |

+--+

Like the original, the big F is to have its center of gravity at the center of rectangle D.

Solving for this F is just like the original F, just more variables. Remarkably the lengths of y and z are both equal to (2x + 1 + sqrt[8x^2 + 16x + 9])/2