Step 1
we know that
the area of a rectangle is equal to
where
x is the length side of the rectangle
w is the width side of the rectangle
<u>Find the total required area</u>
so
------> equation A
Step 2
<u>Find the equation of the perimeter of the rectangular pen</u>
we know that
the perimeter of the rectangle is equal to
Remember that one side of the pen is along a straight river
so the perimeter is equal to
------> equation B
Step 3
Find the minimum amount of fencing
we know that
the minimum amount of fencing is when the perimeter is a minimum
Substitute equation A in equation B
Using a graphing tool
see the attached figure
The vertex of the graph is the point for a minimum perimeter
the vertex is the point
that means
for
The minimum perimeter is equal to
<u>Find the value of y</u>
therefore
<u>The answer is</u>
the minimum amount of fencing he must use to build his pen is