An unfenced rectangular plot of land with an area of 15000 square feet is to be split up into two rectangular gardens. Find the minimum amount of fencing required to define and separate these two gardens? Where do I begin? I just want to know how to set up the equation to figure out the problem.

Answer 1

you ant two rectangles with one side in common. So, if the big plot has dimensions x and y, then

xy = 15000

Now, there will be two sides of length x and 3 sides of length y/3 (because of the extra fence down the middle), so the amount of fence is

f = 2x+3y = 2x + 45000/x

Now just find where df/dx is zero, and that will give you the dimensions for minimum fence.

Expect that when you are all done, the fencing will be divided among the lengths and widths. That is, you will see that 2x=3y.