Precalculus

A farmer with 10000 meters of fencing wants to enclose a rectangular field and divide it into two plots with a fence parallel to the sides. What is the largest area that can be enclosed?

  1. 👍 0
  2. 👎 0
  3. 👁 119
  1. He has 10 km of fence to fence in a field on a farm ??
    Anyway ...

    Let each of the lengths be y
    let each of the shorter sides by x
    so we need 2y + 3x
    2y + 3x = 10000 ---> y = (10000-3x)/2

    area = xy
    = x(10000-3x)/2
    = 5000x - (3/2)x^2
    d(area)/dx = 5000-3x
    = 0 for a max of area
    3x = 5000
    x = 5000/3 m or 1666 2/3 m
    sub that into area
    then area = 4,166,666.667 m^2

    1. 👍 0
    2. 👎 1
    posted by Reiny
  2. lika sum bodee

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    a farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclose?

    asked by kayla on October 26, 2008
  2. 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

    asked by Mary on January 22, 2012
  3. 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

    asked by Kelsie on July 11, 2013
  4. Pre calc

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

    asked by richelle on October 30, 2014
  5. Geomtry

    A farmer has 1000 meters barbed wire with which he is to fence off three sides of a rectangular field, the fourth side being bounded by a straight canal. how can the farmer enclose the largest field?

    asked by AwA on July 16, 2013
  6. Geometry

    A farmer uses 140 ft. of fencing to enclose a rectangular field. if the ratio of length to width is 3:4, find the diagonal of the field. Any help is appreciated, thank you!

    asked by Rachel on November 7, 2010
  7. math

    To enclose rectangular field whose area is 68200 square meter, a farmer used 1460 m of fencing material. What is the length and width of the field. Please answer.. Thank you

    asked by Nimuel on August 14, 2016
  8. math

    A total of 800m of fencing material is used to enclose a rectangular field and to divide the field into four partitions by fences parallel to the width of the field. Find the dimensions of the largest are of the field that can be

    asked by dsadsad on July 26, 2014
  9. 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?

    asked by Janice on June 24, 2015
  10. Algebra 2

    A farmer wants to enclose 2 adjacent rectangular regions next to a river. No fencing will be used next to the river. 60 meters of fencing will be used. What is the area of the largest region that can be enclosed. I need all of the

    asked by Brandon on April 22, 2011

More Similar Questions