Results 1 to 5 of 5

Math Help - Rectangular Swimming Pool

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Rectangular Swimming Pool

    A rectangular swimming pool has length 30 m by 20 m. There is a deck of uniform width surrounding the pool. The area of the pool is the same as the area of the deck. Write a quadratic equation to model this situation and use it to determine the width of the deck.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    <----20+2x---->
    _____________
    |...................|...^
    |.....__20__... |....|
    |..x.|........ |...|...|
    |....|.........|30|...30+2x
    |....|_____ |...|....|
    |...................|....|
    |____________|... v


    Pool area = 600m^2

    Deck area = (30 + 2x)(20 + 2x) = 600

     4x^2 +100x - 600 = 0

     x^2 +25x - 150 = 0

    (x + 30)(x - 5) = 0

    x = 5 (width can't be -30)

    width of deck = 20 + 2x = 20 + 10 = 30m.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    but.....

    Quote Originally Posted by nzmathman View Post
    <----20+2x---->
    _____________
    |...................|...^
    |.....__20__... |....|
    |..x.|........ |...|...|
    |....|.........|30|...30+2x
    |....|_____ |...|....|
    |...................|....|
    |____________|... v


    Pool area = 600m^2

    Deck area = (30 + 2x)(20 + 2x) = 600

     4x^2 +100x - 600 = 0

     x^2 +25x - 150 = 0

    (x + 30)(x - 5) = 0

    x = 5 (width can't be -30)

    width of deck = 20 + 2x = 20 + 10 = 30m.
    I thank you for the reply.

    However, I am slightly lost using the FOIL method in this case.

    We have:

    (30 + 2x) (20 + 2x) = 600

    On the left side, I got this:

    4x^2 + 100x + 600 = 600

    I then subtracted 600 from both sides and got this:

    4x^2 + 100x = 0

    How did you get -600 on the left side of the equation?

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    Sorry about that. It should say:

    (30 + 2x)(20 + 2x) = 1200\,\, (because looking at the diagram (30 + 2x)(20 + 2x) is the whole combined area of the deck and pool).

    (30 + 2x)(20 + 2x) = 1200

    4x^2 + 100x + 600 = 1200

    4x^2 + 100x - 600 = 0
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    ok.............

    Quote Originally Posted by nzmathman View Post
    Sorry about that. It should say:

    (30 + 2x)(20 + 2x) = 1200\,\, (because looking at the diagram (30 + 2x)(20 + 2x) is the whole combined area of the deck and pool).

    (30 + 2x)(20 + 2x) = 1200

    4x^2 + 100x + 600 = 1200

    4x^2 + 100x - 600 = 0
    Now it makes sense.

    Thank you for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rectangular swimming pool geometry problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 6th 2011, 09:07 PM
  2. swimming pool problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 11th 2010, 10:03 PM
  3. swimming pool problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 22nd 2009, 03:29 AM
  4. Swimming Pool Border
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: January 13th 2007, 01:45 PM
  5. Swimming Pool Area
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 4th 2005, 07:34 PM

Search Tags


/mathhelpforum @mathhelpforum