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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.

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

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