SOLUTION: One side of the rectangular field is bounded by a river. A farmer has 100m of fencing and wants to fence the other three sides of the field. If he wants to enclose an area of at le
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Question 891969: One side of the rectangular field is bounded by a river. A farmer has 100m of fencing and wants to fence the other three sides of the field. If he wants to enclose an area of at least 800m^2, what will be the max. length of the field along the river. Answer by LinnW(1048) (Show Source):
You can put this solution on YOUR website! The dimensions of the enclosed area
will be width x by length (100-2x).
The length is reduced by the two ends
of the rectangle.
For an area of 800,
x(100-2x) = 800
100x - 2x^2 = 800
add -800 to each side
-2x^2 + 100x -800 = 0
divide each side by -2
x^2 -50x -400 = 0
(x-10)(x-40) = 0
So x = 10 or x = 40
A value of x = 10 will produce the
largest value for length along
the river ( 100 - 2(10)) = 80 meters.
