precalculus

posted by .

A rectangular field is to be enclosed by a fence and divided into three equal rectangular parts by two other fences. find the maximum area that can be enclosed and separated in this way with 1200m of fencing.

  • precalculus -

    let the width of the whole rectangle be x m (there will be 4 of these)
    let the length be y m
    then 4x + 2y = 1200
    2x + y = 600
    y = 600 - 2x

    Area = xy
    = x(600-2x)
    = -2x^2 + 600x

    Now, I don't know if you are studying Calculus.
    If you do, then
    d(Area)/dx = -4x + 600
    = 0 for a max area
    x = 150

    then y = 600 - 2(150) = 300
    and the max area is (150)(300) = 45000

    If you don't know Calculus, complete the square on the above quadratic
    you should end up with
    Area = -2(x-150)^2 + 45000

  • precalculus -

    45000

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    A rectangular field is to be enclosed by a fence. Two fences parallel to one side of the field divide the field into three rectangular fields. If 2400m of fence are available find the dimensions giving the max area.
  2. algebra

    The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of …
  3. Algebra 2

    A Rectangular Field is to be enclosed by a fence and divided into three parts by another fencer. Find the maximum area that can be enclosed and separated in this way with 500 meters of fencing.
  4. Algebra 2

    A Rectangular Field is to be enclosed by a fence and divided into three parts by another fencer. Find the maximum area that can be enclosed and separated i this way with 500 meters of fencing
  5. pre-calc

    area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three parallel …
  6. Math

    a farmer wants to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. if the farmer can only afford 1000 yards of fencing, what dimensions …
  7. Calculus 1

    A rectangular field is enclosed by a fence and separated into two parts by a fence parallel to one of the sides. If 600 m of fencing is available, what should the dimensions be so that the area is a maximum?
  8. cal

    a rancher has 4000 feet of fencing for constructing a rectangular corral. one side of the corral will be formed by a barn and requires no fence. three exterior fences and 2 interior fences partition the corral into 3 rectangular regions. …
  9. calculus (optimization)

    a rectangular study area is to be enclosed by a fence and divided into two equal parts, with the fence running along the division parallel to one of the sides. if the total area is 384 square feet, find the dimensions of the study …
  10. Calculus

    A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the dimensions of the largest field that can be enclosed with 800 feet of fencing. Help me please!!!!!!!!!!! …

More Similar Questions