SOLUTION: A farmer has 120 feet of fencing to be used in the contruction of two identical rectangular pens sharing a common side. Find the dimensions of the pens that will make the total en

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Question 353118: A farmer has 120 feet of fencing to be used in the contruction of two identical rectangular pens sharing a common side. Find the dimensions of the pens that will make the total enclosed area maximum.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

 
Let the area be y

Area = (base)(height)

Base = 2x
Height = h

Let the area be y

y+=+2xh

Sum of fencings = 4x+%2B+3h

4x+%2B+3h+=+120
     
Solve for h

3h+=+120+-+4x

h+=+%28120-4x%29%2F3

h+=+120%2F3+-+expr%284%2F3%29x

Substitute in

y+=+2xh

y+=+2x%28120%2F3+-+expr%284%2F3%29x%29

y+=+expr%28240%2F3%29x+-+expr%288%2F3%29x%5E2%29

y+=+80x+-+expr%288%2F3%29x%5E2%29

y+=+-expr%288%2F3%29x%5E2+%2B+80x

Use the vertex formula for this parabola:

graph%28400%2C400%2C-5%2C35%2C-50%2C700%2C+80x+-%288%2F3%29%2Ax%5E2%29

x-coordinate of vertex = 

h+=+%28120-4x%29%2F3
h+=+%28120-4%2A15%29%2F3
h+=+%28120-60%29%2F3
h+=+60%2F3
h+=+20

So the dimensions are 2x by h or 2(15) by 20 or 

30ft by 20ft.



Edwin