Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook