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Pre-Calculus Help Please

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A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals. Length of adjacent corral 1 is x, width is y. Length of the two corrals together is 2x, width y. Write the area A as a function of x.

Oct 8th, 2014

Let x and y be the length and width of the rectangular corral.

Since the two rectangular corrals are adjacent to each other, let one side of each corral (x) share a common fence.So, their total perimeter is:


Plug-in the given perimeter of the fence.


Then, isolate either of the variable. Let the y be isolated.

`(200-3x)/4 =y`   (Let this be EQ1).

Next, set-up the equation for total area of the two rectangular corrals.


Then, express the right side as one variable. To do so, substitute EQ1.




To determine the dimensions of each rectangular corral that would  maximize area, take the derivative of area.

`A'= (200-6x)/2` 


`A'= 100-3x` 

Then, set A' equal to zero and solve for x.




Next, substitute the value of x to EQ1.



Hence, the length and width of each rectangular corrals is `100/3` ft. and 25 ft, respectively

Oct 8th, 2014

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