SOLUTION: A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and the 10 metres of fencing for the remaining three sides. What dimension will give h

Question 986771: A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and the 10 metres of fencing for the remaining three sides. What dimension will give him the maximum area for the pen?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
wall length =x
long side length=x
short side is (10-x)/2 for each. The sum is 2x+5-(x/2)+5-(x/2)=10
Area is x((1/2)(10-x)=
(10x-x^2)/2=0
by calculus the first derivative is 10-2x=0; x=5
by quadratic,
(10x-x^2)/2=0
vertex of this is -b/2a=5/1=5
The dimensions are 5m X 2.5m=12.5m^2

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