Enclosing a Rectangular Field David has 400 yards offencing and wishes to enclose a rectangular area.(a) Express the area A of the rectangle as a function of thewidth w of the rectangle.(b) For what value of w is the area largest?(c) What is the maximum area?A aestalYOD-austa400

Question
Asked Oct 1, 2019
Enclosing a Rectangular Field David has 400 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 aestal
YOD-austa
400
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Enclosing a Rectangular Field David has 400 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 aestal YOD-austa 400

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Expert Answer

Step 1

A field is in the shape of rectangle.

 

Let the width of the rectangular field be w and the length of the rectangular field is l.

P 400
2(1w) 400
/w 200
/ 200
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P 400 2(1w) 400 /w 200 / 200

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Step 2

Area of the rectangular field is represented as,

A 1xw
(200 )
2001
v - w
=
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A 1xw (200 ) 2001 v - w =

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Step 3

In order to maximize area differen...

d
-(A)
(200w-2)
....)
=200 21v
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d -(A) (200w-2) ....) =200 21v

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