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"A rectangular pasture is subdivided into two equal pens. Using the barn as one side and 132 m of fencing for the rest, find the value of x that gives the maximum area, and A(x)."

It gives no diagram whatsoever, so I have no idea if all the sides are the same length or not, etc etc... Can someone show me how to work out this problem please? Any help is GREATLY appreciated!! :D

  • Precalculus -

    The fence will look like a letter E. The open end of the letter E is the face of the barn.
    It does not matter which length x stands for, as long as the total length of the fence is 132 m.

    Let x be one of the three equal sides, and the length of the barn fenced in is 132-3x.
    Total area
    A(x) = x(132-3x)
    A'(x) = 132-6x =0
    Therefore x=132/6=22 m
    The area is x(132-3x)=22(66)=1452 m²
    check: A"(x) = -6 <0, therefore maximum.

  • Precalculus -

    Ohhhh I totally get it now!!! Thanks! :D

  • Precalculus :) -

    Glad that it helped! :)

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