Posted by muffy on Saturday, September 12, 2009 at 12:22pm.
A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?
Does that mean I have to consider it a triangle?

Math  bobpursley, Saturday, September 12, 2009 at 12:30pm
No, make the river one of the side, fence the other three sides.
Area= LW
8000=2W+L
or L=80002W
Area= W(80002W)= 8000w2W^2
You can find the max several ways, graphing is simple. IF you get stuck, repost.

Math  muffy, Saturday, September 12, 2009 at 12:47pm
Thanks. I'm still confused though. I'm not sure how you got
Area= W(80002W)= 8000w2W^2
What happened to the L
Do I need a system of equations?
Sorry, this has got me stumped.

Math  bobpursley, Saturday, September 12, 2009 at 12:52pm
It is a quadratic.
Let y= 8000x2x^2
graph y vs X on your graphing calc, notice where the max is on x
Second method. The parabola goes up to a max then down. Find the intercepts for y=0, those will be symettrical to the parabolic axis, so look for where the midpoint of the intercepts are.
y=x(80002x)
intercepts x=0 , x=4000, so the max will be at x (or width 2000).
then solve for L (80002W).
Third method:
Calculus (in a few years you will master this, just watch now)
Area= 8000x2x^2
d Area/dx=0= 80004x
solve for x, x=2000 at max.

Math  muffy, Saturday, September 12, 2009 at 1:07pm
Ok, thanks so much for your explanations.
So, is the max area 8,000,000?

Math  princess, Thursday, January 19, 2012 at 4:03pm
can you help me with this homework please

Math  mohjee, Friday, January 3, 2014 at 2:34pm
What don't you understand?
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