A farmer wants to fence an area of 1,000,000 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What is the length, in feet, of the shortest side of the rectangle?
A farmer wants to fence an area of 1,000,000 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What is the length, in feet, of the shortest side of the rectangle?
Let the length be 'l', width be 'w', and perimeter be 'p'.
We have:
lw = 1,000,000.
And p = 2l + 2w.
We can re-arrange the first:
w = 1,000,000/l.
And substitute in the second:
p = 2l + 2,000,000/l.
Finding dp/dl and letting it equal 0 will give you a minimum length. Can you continue?