Results 1 to 6 of 6

Math Help - Solve by completing the square

  1. #1
    Junior Member
    Joined
    Jan 2011
    Posts
    49

    Solve by completing the square

    Hello! I would like some help with this task.

    The perimeter of a square and a rectangle are equal. The length of the rectangle is 11 cm and the area of the square is 4 cm ^ 2 more than the area of the rectangle. Find the side of the square.

    Thank you!

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Anna55 View Post
    Hello! I would like some help with this task.

    The perimeter of a square and a rectangle are equal. The length of the rectangle is 11 cm and the area of the square is 4 cm ^ 2 more than the area of the rectangle. Find the side of the square.

    Thank you!

    Let the side of the square be "x".

    Let the width of the rectangle be "y".

    The perimeter of the square is 4x

    The perimeter of the rectangle is 22+2y

    The perimeters are equal, so 4x=22+2y


    The square area is x^2

    The rectangle area is 11y

    x^2=11y+4


    Then you can eliminate y and solve for x in the simultaneous equations..
    or, as your title suggests, substituting for y and completing the square.

    4x=22+2y

    x^2=11y+4
    Last edited by Archie Meade; January 31st 2011 at 11:08 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    Thank you for your help!
    I tried to solve the two equations, however I got the wrong answer. How should I do if i want to solve it by completing the square?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    The square is on the "x" term, so we want to form a quadratic equation with "x".

    This means we need a substitution for y, so we use the linear equation to do that.

    4x=22+2y\Rightarrow\ 2x=11+y\Rightarrow\ y=2x-11

    Use this y in the 2nd equation.


    x^2=11y+4\Rightarrow\ x^2=11(2x-11)+4

    x^2=22x-121+4\Rightarrow\ x^2-(22x-121)=4\Rightarrow\ x^2-11x-11x+121=4

    \Rightarrow(x-11)^2=4


    Take positive and negative square roots...

    x-11=\pm2

    x=11\pm2
    Last edited by Archie Meade; January 31st 2011 at 12:42 PM. Reason: cleaned up
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    I cleaned that up.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    Thank you very much Archie Meade! It helped a lot and I understand everything now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: January 10th 2012, 01:07 PM
  2. Solve by completing the square
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 2nd 2011, 11:48 AM
  3. Solve by completing the square
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 5th 2010, 11:48 AM
  4. Solve by completing the square
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 11th 2009, 09:08 AM
  5. Solve by factoring/completing the square
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 31st 2008, 04:15 PM

Search Tags


/mathhelpforum @mathhelpforum