Let
x---------> the length side of the rectangular area
y---------> the width side of the rectangular area
we know that
the area of the rectangle is equal to
-----> equation
The perimeter of the rectangle is equal to
but remember that the fourth side of the rectangle will be formed by a portion of the barn wall
so
-----> equation
<em>To minimize the cost we must minimize the perimeter</em>
Substitute the equation in the equation
Using a graph tool
see the attached figure
The minimum of the graph is the point
that means for
the perimeter is a minimum and equal to
<u>Find the value of y</u>
The cost of fencing is equal to
therefore
<u>the answer is</u>
the length side of the the fourth wall will be
