anonymous
  • anonymous
If 400 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
It's pretty east to start out. Use the formulas: A = w * h P = 2h + w where P is the perimeter of the fence (400 ft), h is the length of one of the 2 parallel sides, and w is the length of the side that is parallel to the river.
anonymous
  • anonymous
okay so 400 = 2h + w now what?
anonymous
  • anonymous
system of equations?

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anonymous
  • anonymous
so solve for either h or w in that equation and substitute that into the Area formula
anonymous
  • anonymous
okay so w = 200/h
anonymous
  • anonymous
no quite
anonymous
  • anonymous
so 400 = 2h + 200/h
anonymous
  • anonymous
w = 400 - 2h
anonymous
  • anonymous
argh okay ...
anonymous
  • anonymous
so 400 = 2h + (400 - 2h)
anonymous
  • anonymous
so that w should be substituted into the Area formula: A = w * h so A = (400 - 2h) * h
anonymous
  • anonymous
A = 400 -2h^2
anonymous
  • anonymous
A = 400h - 2h^2
anonymous
  • anonymous
and now just find the derivative and set if equal to 0?
anonymous
  • anonymous
and yes. take the derivative, set to 0, and that will give you h. you can find w from that, which will give you the total area
anonymous
  • anonymous
so then h = 100 right?
anonymous
  • anonymous
indeed it does!
anonymous
  • anonymous
is w just the x coordinate at x =100?
anonymous
  • anonymous
i mean y coordinate?
anonymous
  • anonymous
sure. if you're mapping w (y-coord) against h (x-coord).
anonymous
  • anonymous
okay so then my area would be 15000?
anonymous
  • anonymous
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anonymous
  • anonymous
see your whole fence is h + h + w = 400
anonymous
  • anonymous
you know h = 100, so w = 200
anonymous
  • anonymous
so A = w * h = 200 * 100 = 20000
anonymous
  • anonymous
a okay whoops i set the 100 as w instead of h
anonymous
  • anonymous
it happens. hope that helped.
anonymous
  • anonymous
it does thank you

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