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Rectangle optimization - possible text error

  1. Jul 25, 2017 #1
    Hi,
    I may have discovered a textbook error but I'm no calc whiz. I need an assist to find out if the question unintentionally described a square instead of a rectangle.
    I have attached the textbooks solution as well as my attempt at a solution.
    The numbers check out, I just want to make sure before I submit a request for review to the author (my prof). Of course there's always the potential that he's just trying to be a tricky guy. IMG_2067.jpg
     
  2. jcsd
  3. Jul 25, 2017 #2

    Ray Vickson

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    The book's equation
    $$ P(x) = x + \frac{440}{x}$$
    should be
    $$ P(x) = 2x + \frac{440}{x}$$
     
  4. Jul 25, 2017 #3

    SammyS

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    A square IS a rectangle; a rectangle with all sides of equal length.
     
  5. Jul 25, 2017 #4
    Anyone confirm that the answer I got is correct?
     
  6. Jul 25, 2017 #5

    scottdave

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    Yes there was a typo in the middle (x should have been 2x), but they apparently carried it through to get the correct answer. One thing to notice about this problem @quicksilver123 is that if you have a rectangle, and you want to maximize area for a given perimeter, the result will be a square. Or if you want to minimize perimeter for a given area, it essentially the same problem, and the result is a square.
     
  7. Jul 25, 2017 #6

    scottdave

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    Yes Length = Width = sqrt(220) cm. Always remember the units.
     
  8. Jul 25, 2017 #7

    haruspex

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    I don't think it was a typo. There is a band of erasure running near-vertically through several lines of text. It wipes out the portions in bold below:

    for area is A=xy
    We know that xy
    P(x) = 2 x
    P''(x) =
     
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