math

posted by .

a farmer has 400 meters of fence with which to enclose a portion of land. the farmer wants to enclose a rect angular piece of ground that is as large as possible. the land is bordered by water on two sides.

There are three options for the farmer
Option 1) have two sides bordered by the water and two sides by the fence
Option 2) have one side bordered by water and three sides by the fence
Option 3) use fence for all four sides

Construct formula for the area in each of the three options( hint: name one side x)

All I have is ¨x=...¨ Someone please help

  • math -

    (1)
    The sides are x and y, so y = 400-x
    The area is thus a = xy = x(400-x)

    (2)
    If the side x is parallel to the water,
    x+2y = 400, so y = (400-x)/2 and the area is
    a = xy = x*(400-x)/2

    (3)
    x+y=200, so the area is
    a = xy = x(200-x)

    If you need to find the maximum area, just remember that the graph of a is a parabola, with max area at the vertex. So, find the vertex of each parabola.

Respond to this Question

First Name
School Subject
Your Answer

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?
  2. algebra

    A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100 ft. of fence?
  3. algebra

    A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80 ft of fence?
  4. Math (Quadratic Equations)

    A field is bound on one side by a river. A farmer wants to enclose the other three sides of the field with fence in order to create a rectangular plot of land for his cows. If the farmer has 400m of fence to work with, determine the …
  5. Algebra 2

    a farmer has 400 meters of fence with which to enclose a portion of land. the farmer wants to enclose a rectangular piece of ground that is as large as possible. the land is bordered by water on two sides. There are three options for …
  6. Algebra 2

    a farmer has 400 meters of fence with which to enclose a portion of land. the farmer wants to enclose a rect angular piece of ground that is as large as possible. the land is bordered by water on two sides. There are three options …
  7. Algebra 2

    2. a farmer has 400 meters of fence with which to enclose a portion of land. the farmer wants to enclose a rectangular piece of ground that is as large as possible. the land is bordered by water on two sides. There are three options …
  8. 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 land …
  9. Math

    A farmer needs to build a fence to enclose a square plot of land with an area of 200 square yards. To the nearest tenth of a yard, how much fencing does the farmer need?
  10. math

    a gardner having 150 meters of fencing materials wishes to enclose a rectangular plot of land and also erect a fence across the land parallel to two of the sides.find the maximum area he can enclose

More Similar Questions