A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80ft of fence? What should the dimensions of the garden be to give this area? Now I came up with 20ft. by 20ft. with 400 being the maximum area. But the book is saying 40ft. by 40ft. with 1600 being the masimum area. Is the book taking 80 and doubling it because it says the farmer is using one side of the barn but we have to use the whole thing?

Question

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle.  What is the maximum area that the farmer can enclose with 80ft of fence?  What should the dimensions of the garden be to give this area?  Now I came up with 20ft. by 20ft. with 400 being the maximum area.  But the book is saying 40ft. by 40ft. with 1600 being the masimum area.  Is the book taking 80 and doubling it because it says the farmer is using one side of the barn but we have to use the whole thing?

anonymous · Answer

with 80 ft of fence, how can u get the dimension 40 by 40??
i think u r correct

anonymous · Answer

Right.  But it gave me 1/2 of the answer as 40ft by ?  So I thought if you have 40ft the other side is 40ft too?  Correct?  Then for the maximum area you multiply the dimensions.  Correct?

anonymous · Answer

u can get the maximum area when it is a square, so, yeah, length and width should be same

anonymous · Answer

Ok,this is how I worked it.  A=2l+2w, 2l=80-w divide both sides by 2= L=40-w.  Then I did a=lw so, I substituted for l and (40-w)w= 40w-w^w, then I went back to 2l+2w=A  so, A=-w^2+40w, then I factored out -1, so -1(w^2+40w+400, now the 400 comes from completing the square of the middle coefficient (1/2(40)=40/2=20.  So -1(w+20)^2+400 is my answer.

anonymous · Answer

?

anonymous · Answer

Ok, what is your problem?  If your not going to help me, leave me alone.  Because I am not understanding you at all!!