Results 1 to 3 of 3

Math Help - related to area and perimeter

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    13

    related to area and perimeter

    Q. Find the sides of all rectangles having integral sides whose area is numerically equal to the perimeter?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    4, but why?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Well, area = l x w = lw

    Perimeter = 2l + 2w

    When they are equal, we get:

    lw = 2l + 2w

    0 = 2l - lw + 2w

    -2w = l(2-w)

    l = \dfrac{2w}{w-2}

    l = 2 + \dfrac{4}{w-2}

    Since 2 + \dfrac{4}{w-2} must be an integer, w can only be equal to 3,4 or 6. Any larger value will give rise to a fraction.

    Hence, when the width is 3, the length becomes 2+4 = 6

    When the width is 4, the length becomes 2+2 = 4

    When the width is 6, the length becomes 2+1 = 3

    That's it!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. perimeter and area
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 18th 2010, 03:50 PM
  2. Perimeter and Area
    Posted in the Geometry Forum
    Replies: 3
    Last Post: February 10th 2010, 03:19 PM
  3. Area from perimeter is it possible?
    Posted in the Geometry Forum
    Replies: 6
    Last Post: July 20th 2008, 05:25 AM
  4. perimeter and area
    Posted in the Geometry Forum
    Replies: 4
    Last Post: April 8th 2008, 06:02 PM
  5. Area and Perimeter
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 10th 2007, 02:06 AM

Search Tags


/mathhelpforum @mathhelpforum