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## You have a 60-foot roll of fencing and a large field. You want to make two paddocks by continuing the fencing down the middle of a rectangul

Question

You have a 60-foot roll of fencing and a large field. You want to make two paddocks by continuing the fencing down the middle of a rectangular enclosure. What are the dimensions of the largest such enclosure you can make?

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Physics
3 years
2021-08-18T13:55:57+00:00
2021-08-18T13:55:57+00:00 1 Answers
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## Answers ( )

Answer:

The dimension of the largest enclosure is width=10ft and length = 15ft

Explanation:

Let the width of the enclosure = a

Let the length of the enclosure = L

Let the area of the enclosure = A

3w + 2l = 60 …eq1

A = we …eq2

From eq1

2l = 60 – 3w

Put 2l = 60 – 3w in eq2

A = w(60 – 3w)/2

A = w(30 – (3/2)w^2

If A =0 , find the roots.

The maximum will be?

-b/2a this is exactly halfway between the roots

-(3/2)w^2 + 30w =0

-b = -30

2a = -(3/2)

-b/2a = -30/-3

w = 10ft

Put w = 10ft in eq 1

3(10) + 2l = 60

30 + 2l = 60

2l = 60 – 30

l = 30/2

l = 15ft