a farmer is planning a rectangular area for her chickens. the area of the ractangle will be 200 square feet. three sides of the rectangle will be formed by fencing which cost $5 per foot. the fourth side of the rectangle will be formed by a portion of the barn wallm which requires no fencing. in order to minimzie the cost of fencing how long should the fourth side be?

Question

anonymous · Answer

lets get a picture |dw:1406325345854:dw|

anonymous · Answer

total cost is $5x+5x+5y=10x+5y$ and since $xy=200$ you have $y=\frac{200}{x}$

anonymous · Answer

now 
$$C(x)=10x+\frac{40}{x}$$  and you want the minimum

anonymous · Answer

take the derivative set it equal to zero to find the critical points etc

anonymous · Answer

how

anonymous · Answer

derivative set?

anonymous · Answer

take the derivative 
find the critical points by "setting it equal to zero"

anonymous · Answer

that is so confusing oh ym god.

anonymous · Answer

is this a calculus course?

anonymous · Answer

geometry

anonymous · Answer

oh then in that case i have no idea what you are supposed to do

anonymous · Answer

hahahaha oh god ok thanks anyways

anonymous · Answer

i can tell you that the long side which is parallel to the side against the barn will be twice the length of the other two sides 
so it will be 100 and the other two will be 50 each

anonymous · Answer

but doing this using geometry and not calculus is above my level of expertise
i have no idea how to do it using just geometry