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Optimization problem: Folding a triangle to minimize one side

  1. Jan 23, 2009 #1
    1. The problem statement, all variables and given/known data

    The upper right-hand corner of a piece of paper, 12 in by 8 in is folded over to the bottom edge. How would you fold it to minimize the length of the fold? In other words, how would you choose x to minimize y?


    2. Relevant equations

    None so far.

    3. The attempt at a solution

    I haven't a clue how to get started. I know I need to relate the length of y to the length of x and then differentiate and find the minima, but I don't know how to form the initial relationship.
  2. jcsd
  3. Jan 23, 2009 #2


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    Staff: Mentor

    Hint -- use the 8x12" information as part of the equations your write. If x is as shown, then the bottom piece is 8-x, right? What can you say about the angles in the two triangles that are formed by that fold?
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