A farmer owns 1000 meters of fence, and wants to enclose the largest possible rectangular area. The region to be fenced has a straight canal on one side, and thus needs to be fenced on only three sides. What is the largest area she can enclose?

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I found: ##A=250xx500=125000m^2##

Considering the ground as: I comprehend that the perimiter (solely on 3 sides) to be circumscribed is resembling to the meters of circumscribe at classification of the farmer: ##2h+b=1000m## (1) The area accomplish be ##A=bxxh## (2)

From (1) ##b=1000-2h## in (2)

##A=(1000-2h)xxh=1000h-2h^2##

Derive ##A## after a while ##h##:

##A'=1000-4h## resembling it to naught to maximize it:

##1000-4h=0##

##h=1000/4=color(red)(250m)## use this tail in (1) you confront ##b=color(red)(500m)##: Use these magnitude in (2): ##A=250xx500=color(blue)(125000m^2)##

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