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?

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) (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

RELATED QUESTIONS
A farmer decides to enclose a rectangular,using the side of a barn as one side as a... (answered by ikleyn)

4) A farmer decides to enclose a rectangular garden, using the side of a barn as one side (answered by jim_thompson5910)

a farmer decides to enclose a rectangular garden, using the side of a barn as one side... (answered by checkley71)

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of (answered by Fombitz)

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of (answered by josmiceli)

A farmer decides to enclose a rectangular garden using the side of a barn as one side of... (answered by EMStelley)

a farmer decides to enclose a rectangular garden, using the side of a barn as one side of (answered by edjones)

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of (answered by nyc_function)

a farmer decides to enclose a rectangular garden using the side of a barn as one side of... (answered by lwsshak3)

A farmer decides to enclose a rectangular garden, using the side of a barn as one... (answered by ikleyn)