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

2 answers:

4 0

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...

Ksju [112]3 years ago

4 0

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

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