farmer ed has 2,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If farmer ed does not fence the side along the river, what is the largest area that can be enclosed?

Question

campbell_st · Answer

well start by drawing a picture

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so the perimeter is 

P = 2x + l      since there is 2000 meters  of fencing its 

2000 = 2x + l

or making l the subject 

l = 2000 - 2x

now the 

Area = length * width 

or after substituting the length value from the perimeter

A = (2000 -2x) * x 

which is 

$$A = 2000x - 2x^2$$

so all you need to do now is 

1. find the 1st derivative

2. solve the derivative for x

and you'll have the width that gives the max area, substitute it into the perimeter equation for the the length that gives the max area. 

hope this helps