let each of the 2 equal sides by x
let yeach of the 3 equal sides by y
xy = 1,500,000
y = 1500000/x
let the length be L
L = 2x + 3y
= 2x + 4500000/x
dL/dx = 2 - 4500000/x^2
= 0 for a min of L
2x^2 = 4500000
x^2 = 2250000
x = 1500
then y = 1500000/1500 =1000
so L = 2(1500) + 3(1000) = 6000 ft
A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side.
What is the shortest length of fence that the rancher can use?
3 answers
.000000000000001 feet or perhaps the length of the width of a cow. :)
The problem does not make much sense as stated. You could make the field extremely longs and not at all wide and divide it with a little fence in the middle the length of your very short ends.
The problem does not make much sense as stated. You could make the field extremely longs and not at all wide and divide it with a little fence in the middle the length of your very short ends.
Oh, sorry, I thought you meant just the length of that splitting fence.