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Relationships Between Area and Perimeter

 Activity Description Activity Guide

In this activity, students explore the relationships between area and perimeter by fixing one value and maximizing the other.

Mathematical Topics:
Students will explore the relationship between perimeter and area of rectangles, use algebraic language to express the relationship, and the first derivative to maximize the general form of the area equation.

Mathematical Thinking: Students will conjecture a relationship between area, perimeter, and the length of side x and will formalize the relationship using algebraic language.

Technology: Students will use (and create) an interactive template to change the parameters in a maximization problem in order to look for patterns and generalizations.  The template includes scroll bars and a geometrical representation of a rectangle. Students will also use several java applets for supplemental investigations.