math

posted by .

A rectangular play yard is to be constructed along the side of a house by erecting a fence on three sides, using house wall as the fourth wall. Find the demensions that produce the play yard of maximum area if 20 meters of fence is available for the project.

  • math -

    Make a sketch,
    let the width of the field be x,
    let the length of the field be y
    then y + 2x = 20 , (we need only one length)
    y = 20-2x

    area = xy
    = x(20-2x)
    = -2x^2 + 20x

    I don't know at what level of math-study you are.
    If you know calculus, find
    d(area)/dx = -4x + 20 = 0
    x = 5 , then y = 10 for a max area of 50

    If you don't know calculus, complete the square of the quadratic function
    A = -2x^2 + 20x
    = -2(x^2 - 10x + 25 - 25 )
    = -2((x-5)^2 - 25)
    = -2(x-5)^2 + 50

    vertex is (5,50)
    so the max area is 50 when x = 5 , as above

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math Calculus

    Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 ft. Let x be the length of two sides perpendicular to the wall as shown. Write an equation of area …
  2. math

    Kira has feet of fencing. She will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. For the area of the garden to be the maximum, how long should the side opposite …
  3. Calc 1

    An 8 foot tall fence separates Larry's yard from Evan's yard.The fence is 3 feet from Larry's house and runs parallel to the side of his house. Larry wants to paint his house and needs to position a ladder extending from Evan's yard …
  4. Calculus

    A rectangular play area is to be fenced off in a person's yard and is to contain 108 yd^2. The next-door neighbor agrees to pay half the cost of the fence on the side of the play area that lies along the property line. What dimensions …
  5. math

    judy wants to fence the sides of the yard in front of her house . She bought 60m of fence and wants the max area she can fence in . The quad function a(x)=-2x^2+60x, where x is the width of the yard in metres , represent area enclosed …
  6. calculus

    a farmer wishes to fence off a rectangular plot of land, using an existing wall as one of the sides . the total are enclosed must be 600 square yards. the fence on the side parallel to the wall will cost 20$ per yard, while the fences …
  7. calculus help

    Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3 a yard, but she needs to use …
  8. Math

    Ernie wants to fence in a rectangular play yard for his two dogs. He has 12 pieces of fence that are one unit each. What are the dimensions of the largest play yard that Ernie could make?
  9. AP Calculus

    The management of a large store has 1600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining 3 sides, find the area of the largest yard possible.
  10. Calculus 1

    A family wants to fence a rectangular play area alongside the wall of their house. The wall of their house bounds one side of the play area. If they want the play area to be exactly 1600ft^2, what is the least amount of fencing needed …

More Similar Questions