Question 1021185: Please help and show all work.
A rancher has 280 feet of fence with which to enclose three sides of a rectangular field (the fourth side is a cliff wall and will not require fencing). Find the dimensions of the field with the largest possible area. (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side).)
length = feet
width = feet
What is the largest area possible for this field?
area = feet-squared
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 2w + l = 280
l = 280-2w
:
Area(A) = l * w
:
substitute for l in area equation
:
A = (280-2w) * w
A = 280w -2w^2
:
now take the first derivative of A
:
A' = 280 -4w
:
set A' = 0 and solve for w
:
4w = 280
:
w = 70
l = 280 - 140 = 140
:
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length = 140 feet
width = 70 feet
area = 140 * 70 = 9800 square feet
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