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How to find the dimensions of the playground that will enclose the greatest tota

Discussion in 'Small Talk' started by Peter, Nov 25, 2010.

  1. Peter

    Peter Guest

    A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 360 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area.
  2. Sem

    Sem The Last of the Snowmen
    Former Administrator

    Uh hi. I guess if you're asking for help with homework or something? I can't help you :V But I'm just making sure so that other people know, people who can help you.
    #2 Sem, Nov 25, 2010
    Last edited by a moderator: Sep 19, 2013
  3. Shiny Pyxis

    Shiny Pyxis 2016 Singles Football

    it'll be a 60 x 90 playground.
    I'll scan in my (dad's) work later :D

    EDIT: Alright, after talking to my dad today, we were able to come up with two ways to solve this problem. His way is with calculus; derivatives and whatnot. It's with the dA/dy stuff. I solved the problem by solving for the square.

    Anyways, we found two equations because this is a two-variable question. Since the total fencing required is 360 ft., and there's a wall down the middle of it, and if x is the width of the playground and y is the length, then we get the equation 3x+2y=360. Then we find the area, which turns out to be xy. Then you use substitution in the first equation, so that you end up withs something like (360-3x)/2=y.

    So then you plug that in to the second equation, so that A=x((360-3x)/2). Simplify that so that you end up with 180x-3/2x^2.

    This is where my dad and I split, and I'll let you try to figure out what we did from the scan. :3


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