Results 1 to 2 of 2

Thread: extreme trapeze perimeter

  1. #1
    Member
    Joined
    Dec 2008
    Posts
    167

    extreme trapeze perimeter

    A halfcircle with r = 14 cm has a trapeze drawn inside it.


    What is the largest possible perimeter of the trapeze (check the image).

    I have to express the perimeter using only 1 variable (i was thinking c) and then derivate the perimeter and equal it to 0 to get the extremes..

    how to express the perimeter using only c?
    Attached Thumbnails Attached Thumbnails extreme trapeze perimeter-trapeze.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    Posts
    167
    ok I tried something..



    $\displaystyle b^2 = x \cdot 28$

    then the perimeter is equal to:

    $\displaystyle o = a + b + c + d = 2r + 2b + c$

    $\displaystyle c = 28 - 2x $
    $\displaystyle b = \sqrt{28x}$

    therefore:

    $\displaystyle o(x) = 28 + 2\sqrt{28x} + 28 - 2x = 56 - 2x + 2\sqrt{28x}$

    $\displaystyle o'(x) = \frac{1}{2}\cdot 2(28x)^{-\frac{1}{2}} \cdot 28 - 2 = \frac{28}{\sqrt{28x}} -2$


    to find the extremes:

    $\displaystyle o'(x) = 0$
    $\displaystyle \frac{28}{\sqrt{28x}} -2 = 0$

    $\displaystyle 28 = 2\sqrt{28x} /^2$
    $\displaystyle 784 = 112x$
    $\displaystyle x = 7$

    $\displaystyle o(x) = 56 - 2x + 2\sqrt{28x}$

    $\displaystyle o(7) = 56 - 2 \cdot 7 + 2\sqrt{28 \cdot 7} = 42 + 28 = 70$


    To check wether the extreme is max or min:

    $\displaystyle o''(x) = (\frac{28}{\sqrt{28x}} -2)' = 28 \cdot (-\frac{1}{2})\cdot (28x)^{-\frac{3}{2}} \cdot 28 = -\frac {392}{\sqrt{(28x)^3}} (< 0) \Rightarrow Maximum$

    can someone check if I'm right please :P
    Attached Thumbnails Attached Thumbnails extreme trapeze perimeter-trapeze.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A circle blocked in a trapeze
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 13th 2011, 05:09 AM
  2. Approximation by trapeze
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Sep 16th 2010, 03:29 PM
  3. Extreme value distributions
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Aug 12th 2010, 05:32 AM
  4. trapeze rule estimate error
    Posted in the Calculus Forum
    Replies: 0
    Last Post: May 4th 2010, 08:39 AM
  5. Extreme Value Theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Feb 12th 2009, 10:28 PM

Search tags for this page

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum