Question

A rectangular dog pound with three kennels
consists of a rectangular fenced area divided
by two partitions. Determine the maximum
possible area of this pound if 72 yards of chain
link fencing is available for its construction.

Answer 1

First Draw out the figure, you have a rectangle, so Width and Length. We'll choose X to be length, and Y to be width.


The area of a rectangle is what? LengthxWidth so
A= XY
The perimeter is given to us as 72.
2X+2Y = 72.
So
X+Y = 36
X = 36-y.
You can now substitute this back into the area equation.
A = (36-Y)*Y
It asks for the maximum area, so you'll need to find the derivative and set it = 0.
Once you solve the Y value, plug it back in to get X. Remember its asking for area, so you have to Give them X*Y as your final answer

Answer 2

maximized area is found when x=y, i.e when it is a square.
4 panels for the sides Plus 2 additional for partitions all 6 at equal lengths.
72yds/6 = 12 yards panels.
maximun area is 12yd x 12yd = 144 yards^2