Math

A gardener has 120 ft of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing.

1. what dimensions would guarantee a garden with an area of 1350 ft^2?
2. What dimensions would guarantee the greatest area? how much is the greatest area?

  1. 👍
  2. 👎
  3. 👁
  1. two width, each of x
    one length of y
    y + 2x = 120
    y = 120 - 2x

    area = xy
    = x(120-2x)
    = 120x - 2x^2

    1. 120x - 2x^2 = 1350
    x^2 - 60x + 675 = 0
    (x - 45)(x + 15) = 0
    x = 45 or x = -15, the last we will reject

    if x = 45 , y = 30

    2. area = 120 - 2x^2 is a parabola which opens downwards so the vertex will be the maximum .
    the x of the vertex is -120/(-4) = 30
    when x = 30
    y = 120-60 = 60

    A width of 30 and a length of 60 ft will produce the largest area of 1800 ft^2

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Suppose that 32 feet of fencing is available to enclose a rectangular garden., one side of which will be against the side of a house. What dimensions of the garden will guarantee a maximum area?

  2. Math

    The question is: A gardener wishes to create a rectangular bed. There are 70 meters of fencing wire which will be used to fence three sides of the garden bed, with a brick wall forming the fourth side. Calculate the maximum area

  3. Math

    Chris wants to build a fence around his square garden. The garden measures 6 feet on each side. How many fencing material does he need?

  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. math

    A gardener has 720 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.What dimensions would guarantee that the garden has the greatest possible area?

  2. algebra 1

    Charles wants to build a vegetable garden such that three sides of the garden are fenced and the fourth side of the garden will be the existing back fence. He has 30 feet of fencing available. Find the dimensions of the garden

  3. Pre-Calculus

    A rectangular garden with an area of 250 square meters is to be located next to a building and fenced on three sides, with the building acting as a fence on the fourth side. Let x be the length of the side parallel to the

  4. Algebra

    a farmer wants to build a rectangular garden with a river as one side.what is the area of the biggest garden that he can fence with 220 meters of fencing materials?

  1. Algebra

    A homeowner wants to fence a rectangular garden using 60 ft of fencing. An existing stone wall will be used as one side of the rectangle. Find the dimensions for which the area is a maximum

  2. optimization calcus

    A rectangular rose garden will be surrounded by a brick wall on three sides and by a fence on the fourth side. The area of the garden will be 1000m^2. The cost of the brick wall is $192/m. The cost of the fencing is $48/m. Find

  3. College Algebra

    A farmer wants to build a rectangular fence using the side of his barn as one side. He has 200 yards of fencing available. Find the maximum possible area he can enclose with the fence.

  4. pre-calc college

    a certain type of fencing comes in rigid 10 foot long sections. Four uncut segments are to be used to fence in a garden on the side of a building. what value of x will make the garden as large as possible?

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