SOLUTION: Farmer Ed has 900900 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, find t

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Question 1024229: Farmer Ed has 900900 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, find the length and width of the plot that will maximize the area. What is the largest area that can be​ enclosed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = width of rectangular plot in meters
( perpendicular to river )
+900900+-+2w+ = length in meters ( parallel to river )
Let +A+ = area
+A+=+%28+900900+-+2w+%29%2Aw+
+A+=+-2w%5E2+%2B+900900w+
This is a parabola with a maximum because of
the minus sign with +w%5E2+ term
Use the formula:
+w%5Bmax%5D+=+-b%2F%282a%29+
when the from of the equation is:
+A+=+a%2Aw%5E2+%2B+b%2Aw+%2B+c+
+a+=+-2+
+b+=+900900+
+c+=+0+
----------------
+w%5Bmax%5D+=+-900900+%2F+%28+2%2A%28-2%29+%29+
+w%5Bmax%5D+=+900900%2F4+
+w%5Bmax%5D+=+225225+
and
+900900+-+2w+=+900900+-+450450+
+900900+-+2w+=+450450+
-------------------------
the length and width of the plot
that will maximize the area are:
width = 225225 m
length = 450450 m
------------------
The maximum area is:
+A%5Bmax%5D+=+225225%2A450450+
+A%5Bmax%5D+=+1.014526013%2A10%5E11+
( ran out of places on my calculator )
---------------
Here's the plot:
+graph%28+400%2C+400%2C+-200%2C+900.9%2C+-10000%2C+105000%2C+-2x%5E2+%2B+900.9x+%29+
( calibrated in 1/1000's )