1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Optimization of a folded piece of paper

  1. Oct 28, 2009 #1
    1. The problem statement, all variables and given/known data

    If you take an 8.5in by 11in piece of paper and fold one corner over so it just touches the opposite edge as seen in figure (http://wearpete.com/myprob.jpg [Broken]). Find the value of x that makes the area of the right triangle A a maximum?

    2. Relevant equations
    A = 1/2(xy)

    3. The attempt at a solution
    x = sqrt((8.5-y)2-y2)
    A = 1/2(y)(sqrt((8.5-y)2-y2))
    da/dx = ((y2-4.25y)/sqrt((8.5-y)2-y2))+1/2(sqrt(-17y-72.25))
    I know that at da/dx=0 the triangle is maximized but da/dx is undefined at y=0 (y graphically). I am pretty sure my derivative is right but maybe I missed something there. Thanks for taking a look.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 28, 2009 #2


    User Avatar
    Homework Helper

    at y = 0, the area will be zero, so i wouldn't be too concerned about that point

    your method is ok, but could be simplified a bit... try muliplying out the RHS of your equation and simplifyng before substituting in
    [tex] x^2+y^2=(8.5-y)^2 [/tex]

    let 8.5 = c if it makes it easier
    [tex] x^2+y^2=(c-y)^2 [/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook