Math

A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?

Does that mean I have to consider it a triangle?

  1. 👍 0
  2. 👎 0
  3. 👁 1,249
  1. No, make the river one of the side, fence the other three sides.

    Area= LW
    8000=2W+L
    or L=8000-2W
    Area= W(8000-2W)= 8000w-2W^2

    You can find the max several ways, graphing is simple. IF you get stuck, repost.

    1. 👍 0
    2. 👎 0
    👨‍🏫
    bobpursley
  2. Thanks. I'm still confused though. I'm not sure how you got
    Area= W(8000-2W)= 8000w-2W^2

    What happened to the L

    Do I need a system of equations?

    Sorry, this has got me stumped.

    1. 👍 0
    2. 👎 0
  3. It is a quadratic.
    Let y= 8000x-2x^2

    graph y vs X on your graphing calc, notice where the max is on x

    Second method. The parabola goes up to a max then down. Find the intercepts for y=0, those will be symettrical to the parabolic axis, so look for where the midpoint of the intercepts are.
    y=x(8000-2x)
    intercepts x=0 , x=4000, so the max will be at x (or width 2000).
    then solve for L (8000-2W).
    Third method:
    Calculus (in a few years you will master this, just watch now)
    Area= 8000x-2x^2
    d Area/dx=0= 8000-4x
    solve for x, x=2000 at max.

    1. 👍 0
    2. 👎 0
  4. Ok, thanks so much for your explanations.

    So, is the max area 8,000,000?

    1. 👍 1
    2. 👎 0
  5. can you help me with this homework please

    1. 👍 0
    2. 👎 0
  6. What don't you understand?

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible

  2. Algebra

    Farmer Ed has 9,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

  3. College Algebra

    You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river,find the length and width of the plot that will maximize the area. What is the largest area that can

  4. Math

    A pig farmer wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle (see the figure below). There are 940 feet of fencing available to complete the job. What is

  1. Math

    1. A gardener has 140 feet of fencing to fence in a rectangular vegetable garden. Find the dimensions of the largest area he can fence. Find the possible rectangular area he can enclose. 2. Suppose a farmer has a large piece of

  2. calculus

    If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write

  3. Calculus

    A farmer has 1500 feet of fencing in his barn. He wishes to enclose a rectangular pen. Subdivided into two regions by a section of fence down the middle, parallel to one side of the rectangle. Express the area enclosed by the pen

  4. math

    A farmer has 90 meters of fencing and would like to use the fencing to create a rectangular garden where one of the sides of the garden is against the side of a barn. Let L represent the varying length of the rectangular garden

  1. Calculus 1

    If you have 280 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?

  2. math

    A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

  3. calculus help

    Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3 a yard, but she needs to

  4. Math

    A farmer wishes 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 afford only 1600 yards of fencing, what

You can view more similar questions or ask a new question.