math

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.

  1. 👍 0
  2. 👎 0
  3. 👁 443
  1. 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

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    Gerry plans to place a 24-foot ladder against the side of his house. The bottom of the ladder will be 4 feet from the house. How far up the side of the house will the ladder reach? Answer exactly or round to 2 decimal places.

  2. Math

    The drama teacher is making costumes for the school play. Each costume requires 1 and 2/3 yards of material and 3/4 of a yard of ribbon. The material costs $2.99 per yard and the ribbon costs 59 cents per yard. What is the

  3. 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?

  4. Math

    A rectangular dog pen is to be constructed using a barn wall as one side and 60 meters of fencing for the other three sides. Find the dimensions of the pen that maximize the pen's area.

  1. Math

    You are designing a rectangular dog pen off the back of your house. The House will form one side of the dog pen. The pen is to have an area of 800 ft.² but you want to minimize the amount of fencing that you need for the three

  2. Algebra

    Ian wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has 100 feet of fencing available. Find the dimensions that will enclose the maximum

  3. Algebra 2 b

    Jane is going to fence in her back yard. She has purchased 100 feet of fencing and knows that she wants to fence in a rectangular area where one side will be the back of her house. She knows her house is 30 feet across the back.

  4. Math

    The drama teacher is making costumes for the school play. Each costume requires 1 3/4 yards of material and 2/3 of a yard of ribbon. The material costs $2.99 per yard and the ribbon costs 59¢ per yard. What is the approximate

  1. PreCalculus

    A homeowner has forty feet of fencing to enclose three sides of a rectangular patio. The fourth side of the patio is a side of the house, and requires no fencing. 1. Let x represent the side of the rectangle perpendicular to the

  2. Algebra word problem

    A family is building a rectangular patio in their backyard. The rectangular yard has dimensions of (8x+2) by (6x + 3) and they are planning the patio to be (x + 5) by (3x + 1). What is the area of the remaining yard after the

  3. Algebra

    A family is building a new house on a rectangular lot of land. The lot measures 7x by 11x and the house will be 2x by 3x. How much land will be left for their yard after the house is built? (1 point)

  4. 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

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