SOLUTION: A field is bounded on one side by a river. A farmer wants to enclose the other three sides of the field with a fence in order to create a rectangular plot of land for his cows. If

Question 872829: A field is bounded on one side by a river. A farmer wants to enclose the other three sides of the field with a fence in order to create a rectangular plot of land for his cows. If the farmer has 400m of fence to work with, determine the maximum possible area of the field and the field's dimensions.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A field is bounded on one side by a river. A farmer wants to enclose the other three sides of the field with a fence in order to create a rectangular plot of land for his cows. If the farmer has 400m of fence to work with, determine the maximum possible area of the field and the field's dimensions.
.
Let x = width
and y = length
2x+y = 400 (eq 1)
xy= area (eq 2)
.
Solving eq 1 for y:
y = 400-2x
substitute into eq 2
x(400-2x) = area
-2x^2+400x = area
since the above is a parabola that opens downwards, the vertex is the max.
x-value of the max is:
x = -b/(2a)
x = -400/(2(-2))
x = -400/(-4)
x = 100 feet (width)
.
length is:
2x+y=400
2(100)+y=400
200+y=400
y = 200 feet
.
Max area is:100*200 = 20000 square feet
RELATED QUESTIONS
One side of the rectangular field is bounded by a river. A farmer has 100m of fencing and (answered by LinnW)

Farmer Fred wants to fence in a rectangular pasture that is bordered on one side by a... (answered by richwmiller,Alan3354)

A farmer wants to fence in three sides of a rectangular field with 1,000 feet of fencing. (answered by rfer)

Farmer Fred wants to fence in a rectangular pasture that is bordered on one side by a... (answered by Fombitz)

A rectangular field is to be bounded by a fence on three sides and by a straight stream... (answered by ikleyn)

I am so stuck on these type of word problems, can I please get some help? A local farmer... (answered by ewatrrr)

A farmer has 120 meters of fencing and wants to enclose a rectangular plot of land that... (answered by TimothyLamb)

A farmer wants to fence in three sides of a rectangular field with 1000 feet of fencing.... (answered by stanbon,Theo)