SOLUTION: a farmer has 34m of fencing. he wants to pen in some animals. what is the maximum area he can enclose with this length of fencing, using a regular quadrilateral pen?

Question 751575: a farmer has 34m of fencing. he wants to pen in some animals. what is the maximum area he can enclose with this length of fencing, using a regular quadrilateral pen?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Perimeter = 2 lengths + 2 widths
2l + 2w = 34m
Therefore 2l = 34 - 2w
l = 17 - w
Area = length x width
( 17 - w) x w
17w - w^2
Differentiate
17 - 2w
17 - 2w = 0
- 2w = - 17
w = 8.5
By inserting values below and above 8.5 into 17 - 2w
the value 8.5 is found to be a maximum.
length = 8.5
width = 8.5
Max area = 72.25 m^2

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