precalculus

A rectangular garden next to a building is to be fenced with 120 feet of fencing. The side against the building will not be fenced. What should the lengths of the other three sides be in order to assure the largest possible area?

  1. 👍 0
  2. 👎 0
  3. 👁 234
asked by gilly
  1. 2 w + L = 120 so L = (120-2w)

    A = w L = w (120-2w) = 120 w - 2w^2
    y = A/2 = 60 w - w^2
    maximize A/2 same as max A
    w^2 - 60 w = -y

    w^2 - 60 w + 900 = -y + 900

    (w-30)^2 = -(A/2) + 900
    vertex at w = 30
    the L = 120-60 = 60
    so
    30, 30 and 60

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. wow you rock thanks a bunch x

    1. 👍 0
    2. 👎 0
    posted by gilly

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A rectangular garden is to be fenced off and divided into 3 equal regions by fencing parallel to one side of the garden. 200 feet of fencing is used. find the dimensions of the garden that maximizes the total area enclosed. what

    asked by Usman on June 15, 2011
  2. 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
  3. College Algebra

    A rectangular garden next to a building is to be fenced on three sides. Fencing for the side parallel to the building costs $60 per foot, and material for the other two sides costs $20 per foot. If $1,500 is to be spent on

    asked by Zach on March 26, 2015
  4. 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

    asked by Courtney on January 18, 2008
  5. 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
  6. math

    a rectangular garden is to be fenced along four sides and in the middle it is to be divided into 2 equal areas.if 300meters of fencing materials is available, find the maximum possible area that can be fenced.

    asked by Anonymous on December 2, 2011
  7. Maath:)

    Sam is going to plant a rectangular flower garden next to his house. There will be a fence on three sides of the garden( fencing is not necessary along the houe). The area of the garden is to be 1,000sq. ft., and he has 90 feet of

    asked by Honey on April 30, 2012
  8. 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
  9. Algebra 2

    Ann wants to plant a rectangular garden next to a straight river. She has 120 feet of fencing and will not fence the side of the garden next to the river. What dimensions will produce the largest garden?

    asked by Carolyn on April 23, 2012
  10. 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?

    asked by angel on September 27, 2019

More Similar Questions