Math

A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can be enclosed? (Note: The side along the barn will not require fencing)

  1. 👍
  2. 👎
  3. 👁
  1. let the width of the field be x ft
    let the length be y ft
    so y + 2x = 80
    or y = -2x + 80

    area = xy
    = x(-2x+80)
    = -2x^2 + 80x

    do you know Calculus?
    if so ...
    d(area)/dx = -4x + 80 = 0 for a max area
    4x = 80
    x = 20
    width is 20 ft, length is 40 ft.
    largest area = 20(40) = 800 ft^2

    If you don't know Calculus, complete the square

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc.

    Please help solve this, A farmer has 600m of fence and wants to enclose a rectangular field beside a river. Determine the dimensions of the fence field in which the maximum area is enclosed. (Fencing s required on only three

  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. 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?

  4. Calc

    A rectangular page is to contain 30 sqaure inches of print. The margins on each side are 1 inch. Find the dimensions of the page sucha that the least amount of paper is used. A farmer plans to fence a rectangular pasture adjacent

  1. 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

  2. math

    a farmer has enough fencing to build 40 feet of fence. He wishes to build a rectangular pen nest to his barn wall forming one side of the pen. What dimension should he make the pen so as to enclose the greatest possibility area?

  3. 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

  4. intermediate algebra

    A farmer with 3000 feet 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?

  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. Math

    4. Megan wants to build a fence around her pool. The pool is 28 feet long by 23 feet wide. The fence is to be 15 feet from the edge of the pool. A What are the outside dimensions of the area surrounding the pool B how many feet of

  3. ALGEBRA

    A farmer has 165 feet of fencing material in which to enclose a rectangle area. He wants the length x to be greater than 50 feet and width y to be no more than 20 feet. write a system to represent this situation.

  4. 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

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