Greenwood press

MATRICES
63

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Transformation matrices and robotics

Viewing objects in computer graphics

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PERIMETER
The distance around an object, or perimeter, is used for many purposes. The
concept is used by construction workers to determine the amount of trim needed
to seal the intersection between the drywall and ground, and drywall and ceiling
in each room when building a house. Artists use perimeter to determine the
amount of material they will need to put a frame around their pictures.
Homeowners use perimeter to determine the amount of fencing they would
need for their back yard, or railroad ties to surround an outdoor patio. In an open
field, a farmer can determine that the most ideal arrangement for building a rec-
tangular pen for animals is to place his fencing in the form of a square. Suppose
the farmer has 80 meters of fencing. In a rectangular pen, the unknown dimen-
sions of the length and width can be represented by variables, l and w, respec-
tively. The perimeter of the rectangular pen can be written as 80 = 2l + 2w.
The equation can be reduced to
l + w = 40 by dividing both sides of the equa-
tion by 2. Ideally, the farmer would like to build the largest pen so that his animals
have the greatest amount of space to move around in. Thus the farmer needs to
determine the dimensions that would produce a maximum area. The area, 
a, can be
represented by the equation 
a = lw. Substituting the perimeter relationship
l = 40 − w, the area equation can be rewritten as a = (40 − w)w = 40w − w
2
.
A graph of this function shows that the area attains a maximum value when the