#### Perimeter Ratio

The perimeter ratio of a department is the ratio of the current perimeter length divided by the perimeter of a square department with the same area. Let and
be the perimeter and area of department *i*, respectively, the perimeter ratio is then given by:
(3.2)

For example the perimeter ratio of a square is one and the perimeter ratio of a four by one rectangle is equal to 1.25. A higher value indicates a department with a more convoluted shape.

For rectangular departments, the perimeter can be expressed in function of the width and length of the department as:

(3.3)

The perimeter ratio is an output variable, computed by the program based on the current shape of the department.

For rectangular departments there exists a one to one correspondence between the perimeter and shape ratio of a department. Let be the shape ratio of a department, then this
relationship is given by:

(3.4)

The equivalent values for the most practical range of the shape and perimeter ratio are given in the following table.

*Table 3.1. Equivalent Values of Shape and Perimeter Ratios for Rectangular Departments*