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

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



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) About Me  (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
graph%28300%2C300%2C-10%2C10%2C-10%2C20%2C-0.5x%5E2%2B5x%29