A regulation NFL playing field of length x and width y has a perimeter of 3462 / 3 or 1040 / 3 yards.
(a) Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle.
(b) Show that the width of the rectangle is y = 520/3 - x and its area is A = x( ( 520/3 − x) ) .
(c) Use a graphing utility to graph the area equation. Be sure to adjust your window settings.
(d) From the graph in part (c), estimate the dimensions of the rectangle that yield a maximum area.
(e) Use your school's library, the Internet, or some other reference source to find the actual dimensions and area of a regulation NFL playing field and compare your findings with the results of part (d).