let the length parallel to the barn be y ft
let the two other sides be x ft each
so 2x + y = 120
y = 120 - 2x
area = xy
= x(120-2x)
= -2x^2 + 120x
this is a downward parabola,
the x of the vertex is -b/2a = -120/-4 = 30
then y = 120-60 = 60
So the largest area is 30(60) or 1800 ft^2
when the long side is 60 ft and the short side is 30 ft
check:
available fence = 120 ft
one long side + 2 short sides = 60 + 2(30) = 120
suppose we use 29 ft for the short side, then the longer side is 120-2(29) = 62
and the area is 29(62) = 1798 which is less than 1800
suppose we use 31 ft for the short side, then the longer side is 120-2(31) = 58
and the area is 31(58) = 1798 which is less than 1800
A farmer has 120 feet of fencing to enclose a rectangular plot for some of his animals. One side of the area borders on a barn.
a.) If the farmer does not fence the side along the barn, find the length and width of the plot that will maximize the area?
b.) What is the maximum area that can be enclosed?
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I'm not sure if this is even close to how part a) should start but is it 2x+y=120? I'm confused.
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