Diana has available 120 yards of fencing and wishes to enclose a rectangular area.
(a) express the area a of the rectangle as a function of the width w of the rectangle.
(b) for what value of w is the area largest?
(c) what is the maximum area?

a) Area = 60W - W²

b)  For maximum area, W = 30 yards

c) Maximum area = 900 yard²

Step-by-step explanation:

Diana has available 120 yards of fencing and wishes to enclose a rectangular area.

Let L be the length and W be the width.

Perimeter of rectangle = 2 ( L + W) = 120

                          L + W = 60

                           L = 60 - W

a) Area, A = Length x Width = (60 - W) x W = 60W - W²

b) For maximum area we have

   For maximum area, W = 30 yards

c) Area = 60W - W² = 60 x 30 - 30² = 900 yard²

   Maximum area = 900 yard²