posted by .

A rectengular area is to be enclosed on three sides by fencing, an existing hedge forming the fourth side. Find the greatest area of the rectangle and its dimensions if 140mof fencing is available.

  • Math -

    let the length parallel to the hedge be y
    let the width be x

    so y + 2x = 140
    y = 140-2x

    area = xy
    = x(140-2x) = -2x^2 + 140x

    if you know Calculus:
    -4x + 140 = 0
    x = 35
    then y = 140 - 70 = 70

    max area = 35(70) = 2450

    If no Calculus:
    complete the square to find the vertex

    A = -2x^2 + 140x
    = -2(x^2 - 70x)
    = -2(x^2 - 70x + 1225 - 1225)
    = -2( (x-35)^2 - 1225)
    = -2(x-35)^2 + 2450
    so the vertex is (35,2450)
    giving us a max of 2450 when x = 35

  • Math -

    IDK but I'm not in eight grade, YET!! Comment, share, and love My pro in Facebook. Find me as Jessi Vertiz

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Applied Math- Gr.11

    A farmer wants to enclose three sides of a rectangular pasture unsing 1000 yards of fencing. The fourth side does not require fencing because it borders a river. What dimensions (length and width) should the farmer choose in order …
  2. word problem?

    A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. Two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on the side opposite the wall. The two remaining sides will …
  3. 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 that …
  4. Polynomials and quadratic application

    I want to make a rectangular garden by fencing in a area on the back of my house. Three sides of the rectangle will be fencing; the fourth side will be the side of the house. I have 60 feet of fence. What dimensions should I make the …
  5. Math

    A rectangular livestock pen with THREE SIDES of fencing is to be built against the barn. The fencing is 1050ft long. Find the dimensions of the maximum area that can be enclosed. What is the maximum area?
  6. Math: Optimising

    cant figure out this homework question! I need to use optimisation to find the answer but I cant work it out :( There is a rectangular garden which is in need of fencing. Three sides of the 30m wide garden are already fenced. You own …
  7. math

    A farmer wants to fence in three sides of a rectangular field shown below with 880 feet of fencing. The other side of the rectangle will be a river. If the enclosed area is to be maximum, find the dimensions of the field.
  8. Math: Word Problem

    A security fence encloses a rectangular are on one side of a park in a city. Three sides of fencing are used, since the fourth side of the area is formed by a building. The enclosed area measures 450 square feet. Exactly 60 feet of …
  9. Algebra

    A rectangular pig pen is made of 84 meters of fencing on three sides. The fourth side is a barn wall. Find the dimensions and greatest possible area of the enclosure.
  10. Math(Reiny Please Help)

    Lacy has $600 set aside to build a rectangular exercise kennel for her dogs. She will buy fencing material for $15/ft. Because the side of an existing barn will be used for one of the sides of the kennel, only three sides need to be …

More Similar Questions