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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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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