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Finding the trapezoid of smallest perimeter given a,b,h

  1. Jan 5, 2009 #1
    Hi all,

    It seems obvious that the trapezoid with the smallest perimeter given the lengths of the bases and the height is the isosceles trapezoid. How can I prove this (preferably using analytical methods)?

    Note: this is not homework or anything. I need to know this as a step to prove the answer to a larger problem that I'm solving for my own pleasure, not for school.

    Thanks for the help.
     
  2. jcsd
  3. Jan 5, 2009 #2

    tiny-tim

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    Hi uman! :smile:

    Cut out the clutter …

    draw the two obvious triangles, then cut out the rectangle in between, and move the triangles together to make a new triangle …

    now all you need is to minimise the perimeter of this new triangle. :wink:
     
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