A rancher uses 834 meters of fencing to enclose a rectangular region and also to subdivide the region into two smaller rectangular regions by placing a fence parallel to one of the sides. Find the dimension that produce the greastest enclosed area.
We might as well put the subdivision right in the middle and
divide the rectangle into two equal x by h rectangles.
Let the area be
Area = (base)(height)
Base =
Height =
Let the area be
Sum of fencings =
Solve for h
Substitute in
Use the vertex formula for this parabola:
x-coordinate of vertex =
So the dimensions are 2x by h or by or
m by m
or
210.75m by 140.5m
Edwin