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?

Answer 1

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