A child-care center has 200 feet of fencing to enclose two adjacent rectangular safe

Chapter 3, Problem 64

(choose chapter or problem)

Algebraic-Graphical-Numerical

A child-care center has 200 feet of fencing to enclose two adjacent rectangular safe play areas (see figure). Use the following methods to determine the dimensions that will produce a maximum enclosed area.

(a) Write the total area A of the play areas as a function of x.

(b) Use the table feature of a graphing utility to create a table showing possible values of x and the corresponding total area A of the play areas. Use the table to estimate the dimensions that will produce the maximum enclosed area.

(c) Use the graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area.

(d) Write the area function in standard form to find algebraically the dimensions that will produce the maximum enclosed area.

(e) Compare your results from parts (b), (c), and (d).