Hi, i m Vishal from India and i m having trouble solving this problem from the notes of complete algebra from freecodecamp’s video notes which was uploaded in 2018
A rancher plans to build a rectangular corral according to the plan shown
in the diagram.
If the rancher has a total length of 800 feet of fencing, determine the dimensions that
will allow for the maximum enclosed area.
What have you got so far? This looks like a calculus problem
Sorry sir but its a not a calculus problem but a quadratic function problem
Ok, I can see how that would be a valid tool to use.
Still, what have you tried so far?
I have taken (x) representing width of each rectangular section (including 3 fencing in between)
then taken total perimeter for all four rectalgles combined
as 4x+5y=800
solved the perimeter equation for y y=(800-4x)/5
then enclosing the area as Area=x*y
then substituting it for y from the perimeter equation: [Area=x*((800-4x)/5)
then to find the max area , we’ll complete the square for the quadratic equation:
Area= 1/5(800x-4x^2)
Area= (-4x^2/5) + 160x + 0
completing the sq. by using the formula (b/2)^2
this is the last stage where i have tried so far
classNotes_m110_2018F.pdf (unc.edu)
page 176
You’ve got the right process, but you have a small bug with your calculations.
If a single rectangle is Y units tall and X units wide, the area of a single enclosure would be X * Y and the perimeter would be 2 X + 2 Y.
So here, the total perimeter is 8 X + 5 Y.
With that as the perimeter, what would be the new formula for area?
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