Diana has available 1600 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 the largest?

c). What is the maximum area?

The required function is .

The value of W is 400 yd.

The maximum area is 160000 yd².

Step-by-step explanation:

Diana has available 1600 yards of fencing and wishes to enclose a rectangular area.

Let L be the length and W be the width of rectangle.

The perimeter of the rectangular area is 1600 yards.

i.e.

a) Express the area A of the rectangle as a function of the width W of the rectangle.

The area of the rectangle is

So, the required function is .

b) For what value of W is the area the largest ?

The area is largest when

From (a) the value of a=-1 and b=800

Substitute,

So, the value of W is 400 yd.

c) What is the maximum area?

For maximum area substitute the value of W=400 in area,

So, the maximum area is 160000 yd².

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step-by-step explanation:

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