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?

Question

Physics

Nibbles

7 November, 23:24

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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Answers (1)

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Lesly Newman · Answer 1

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