SOLUTION: 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?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 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?       Log On


   

Question 258781: 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 the area?
The maximum area that the farmer can enclose with 80ft. of fence is ? sq ft.
The dimensions of the garden to give this area is 40 ft. by ? ft.
Thank you in advance for your help with this problem.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Total perimeter will be 80+B=p
2L+2B=p
80+B=2L+2B
80=2L+B
if b=50 then
80=2L+50
30=2L
L=15
A=50*15=750
if b=30 then
80=2L+30
50=2L
25=L
A=30*25=750
So A peaked at B=2*(50-30)=40
80=40+20+20
b=40
80+40=120
40+(40+20+20)
sides 40 and 20
40*20=800
maximum area 800 sq ft
40*20