can soome one find me the answers to these to question ...i have been banging my head gor bout 2 hours?

Question

1)A rancher wants to fence in an area of 3,800,000 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?

2)A rancher wants to fence in an area of 580 square feet in a rectangular field using fencing material costing 1.3 dollars per foot, and then divide it in half down the middle with a partition, parallel to one side, constructed from material costing 0.6 dollars per foot.
Assuming that the partition is parallel to the side which gives the width of the field, find the dimensions of the field of the cheapest design.
find the Lenght and Width and the cheapest design

Answer 1

Answer to both questions relates to minimizing the perimeter. The shape with the minimum perimeter per unit area is a circle. Since the field must be a rectangle, the closest you can get to a circle is a square. For #1, when you divide the field in half, it complicates things. You need to write an equation that relates the area (which is given) to the perimeter, including the fence down the middle. For a square, area is L*W and L=W. For this field, the perimeter (fence length) is 2*L+2*W+1*W (to cut it in half). So you know that L*W = the area A. Rearrange so you can substitute A/W for L in the perimeter eqn. Rearrange that and you will have a quadratic eqn relating Area to Perimeter. Find minium of that eqn.