Math

You want to build a garden around your garden. One side borders your house so it does not need a fence. If you only have 50m of fencing what dimensions should you make your garden in order to maximize the area?

  1. 👍 0
  2. 👎 0
  3. 👁 106
asked by Ashlee
  1. Let the side parallel to the house by y
    the each of the other two sides be x
    Make a sketch

    2x + y = 50
    y = 50-2x

    area = xy
    = x(50-2x)
    =50x - 2x^2

    the x of the vertex of this parabola is -b/(2a) = -50/-4 = 12.5

    so x = 12.5
    and y = 50-25 = 25

    The garden should be 25 m long and 12.5 m wide

    by Calculus:
    area = 50x - 2x^2
    d(area)/dx = 50-4x = 0 for a max of area
    4x=50
    x = 12.5
    continue as above

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by sridhar on September 13, 2009
  2. math

    3) You are fencing a rectangular puppy kennel with 25 ft of fence. The side of the kennel against your house does not need a fence. This side is 9 ft long. Find the dimensions of the kennel. 4) A gardener is planning a rectangular

    asked by name on April 27, 2017
  3. Math

    Your grandmother has asked you to help her build a rectangular garden for her roses in her back yard. She has 120 feet of fencing and plans to have one side of the garden against the back of her house so it doesn’t need fencing.

    asked by Emm's browser on March 20, 2019
  4. Math

    sam decides to build a square garden if the area of the other garden is 9x^2 -24x +16 square feet what is the length of one side of the garden

    asked by Helpmelol on March 6, 2018
  5. Mathematics

    Mary wants to build a fence around a rectangular area for a garden. She has 150 ft of fencing and she wants to leave 10 ft opening on side for a gate. In order to make a area of the garden. A maximum what should the dimensions of

    asked by Leian on January 20, 2016
  6. Algebra

    a rectangular garden is located adjacent to a house the family needs to fence in the garden the family wants three side because one side is up against the house the length is 5 meters longer than the width and the area of the

    asked by Kay on September 8, 2012
  7. Math

    A rectangular garden is to be fenced by a farmer. One side of the garden is next to the wall of the house and need not to be fenced. Find the dimensions of the largest garden that can be enclosed with 100m of fencing.

    asked by Agnes on August 28, 2014
  8. math

    zack is planning to make a flower garden he has 24 one yard sections of fence that he plans to place around garden he wants the garden to be aas long as possible what longest length he can use for the garden how wide will the

    asked by aron on May 9, 2016
  9. Math

    You have 7L feet of fence to make a rectangular vegetable garden alongside the wall of your house, where L is a positive constant. The wall of the house bounds one side of the vegetable garden. What is the largest possible area

    asked by Lou on March 21, 2019
  10. Calculus 1

    You have 8L feet of fence to make a rectangular vegetable garden alongside the wall of your house, where L is a positive constant. The wall of the house bounds one side of the vegetable garden. What is the largest possible area

    asked by Sofia on March 26, 2018

More Similar Questions