Question

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?

Answer 1

500ft of fencing is available to enclose a rectangular area 10ft along a highway. Only 3 sides are needed. What dimensions will produce an area of 40000? What is the maximum area that can be enclosed...

Answer 2

Answer:

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

                     $\frac{dA}{dW}=0\\\\\frac{d}{dW}\left ( 60W - W^2\right )=0\\\\60-2W=0\\\\W=30$

   For maximum area, W = 30 yards

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

   Maximum area = 900 yard²