SOLUTION: You have 200 feet of fencing material to make a pen for live stock. If you make a rectangular pen, what is the maximum aree you can fence in? Extend the table to determine the

Question 431927: You have 200 feet of fencing material to make a pen for live stock. If you make a rectangular pen, what is the maximum aree you can fence in?
Extend the table to determine the anser.
Base=3 Permimeter=200 Height=? Area=?
Base=20 Perimeter= 200 Height=? Area=?
I need help finding out the height and Area.
Help me Please & Thank you (:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The perimeter of the pen is 2l + 2w
The area of the pen is l*w
Given: 200 feet of material
So we can write
200 = 2l + 2w -> l + w = 100 -> l = 100 - w
Substitute this value for l in the equation for the area:
A = w(100-w)
This area will be maximized for dA/dw = 0
dA/dw = 100 - 2w
Set=0 and solve for w:
2w = 100 -> w = 50
So the length is also 50.
Therefore, the maximum area = 50*50 = 2500 sq. ft.
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