SOLUTION: Fred wants to construct a rectangular chook pen, using a barn for one of the sides (length). the other sides will be constructed using only 80 metres of chicken wire. How long and

Question 668845: Fred wants to construct a rectangular chook pen, using a barn for one of the sides (length). the other sides will be constructed using only 80 metres of chicken wire. How long and how wide should the pen be to enclose as much land as possible (write an algebraic function that will determine the area of the pen in terms of its width and use it to find the answer).
I have currently worked out that the three sides will equal;
width (x2)= 20m
length (x1)= 40m
area= 800m^2
If i could please have some help working out the algebraic function and the solution.
thankyou very much!

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Fred wants to construct a rectangular chook pen, using a barn for one of the sides (length). the other sides will be constructed using only 80 metres of chicken wire. How long and how wide should the pen be to enclose as much land as possible (write an algebraic function that will determine the area of the pen in terms of its width and use it to find the answer).
**
let x=length
y=width
x+2y=80
2y=80-x
y=(80-x)/2
..
Area=f(A)=length*width=xy
=x(80-x)/2
=(80x-x^2)/2
f(A)=-1/2(x^2-80x)
complete the square
f(A)=-1/2(x^2-80x+1600)+800
f(A)=-1/2(x-40)^2)+800
This is an equation of a parabola that opens downward with a maximum of 800 at x=40
x=40
y=(80-x)/2=20
to enclose as much land as possible:
length=40 metres
width=20 metres
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