SOLUTION: If a farmer needs to enclose a rectangular space with a total area of 575 sq yd next to a cliff and the side next to the cliff does not need fencing, what is the least amount of fe

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Question 815228: If a farmer needs to enclose a rectangular space with a total area of 575 sq yd next to a cliff and the side next to the cliff does not need fencing, what is the least amount of fencing necessary to enclose this area?
Total fencing:_______________yd
Length parallel to th cliff:____________yd
Length perpendicular to th cliff:__________ yd
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y. Side lengths for the rectangle shape.

xy=575, and 2x%2By=p for perimeter. This uses y as the side parallel to the cliff.

p is a function of x and y.
y=575%2Fx so substitute:
p=2x%2B575%2Fx---------Now, p is expressed as just a function of x.

You could try graphing this with some software and look for the x value at which p is the smallest value. You might also try taking the derivative of p versus x, set this equal to zero, and find the value for x. You should find something near x=16.5, not sure exactly the value (I used google search for the function and found an interactive graph.)