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Thread: Some charade.2673 days old

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    Hug a Pit! Yautja_BR's Avatar
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    Default Some charade.

    The side AD (measuring 1) of the the square ABCD is strechted to form the segment AE so B, F and E are collinear. If the segment EF measures 1, obtain the the value "x" of the segment DE. (see picture in the link).

    http://4.bp.blogspot.com/_6mIFPN9tgm...0/TRANGULO.JPG






    Hint: It's not 1. Also F is not the midpoint of the segment CD, so making FD 1/2 will not work.
    Last edited by Yautja_BR; 2012-06-28 at 14:26.

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    Scientia potentia est Vadim Verenich's Avatar
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    The way I see it, there're two types of people: those who spend their lives trying to build a future. And those who spend their lives trying to rebuild the past.

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    Quote Originally Posted by Vadim Verenich View Post
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    Try the link now

    Anyone?

    Another hint: Don't use the pythagoren theorem as it won't work in this particular case.
    Last edited by Yautja_BR; 2012-06-28 at 15:03.

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    Ok.

    0,75
    Last edited by Vadim Verenich; 2012-06-28 at 16:38.
    The way I see it, there're two types of people: those who spend their lives trying to build a future. And those who spend their lives trying to rebuild the past.

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    Yautja_BR (2012-06-28)

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    Quote Originally Posted by Vadim Verenich View Post
    Ok.

    0,75
    Did you find this value through a quadratic equation?

    Looking at the vertex E and its angle "a" (let's the call it "a") is the same for both the triangle ABE and the triangle DFE. So they're similar.

    From the triangle ABE we have the tangent: 1/1+x;

    From the triangle DFE we have its secant: 1/x, which is the inverse of the cosine. The relation tga^2+1=seca^2 gives us:

    (1/1+x)^2+1=(1/x)^2.
    Last edited by Yautja_BR; 2012-06-28 at 17:35.

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    Another hint: The expression above will eventually lead us into a quadratic equation.

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    The answer is 42.

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    Quote Originally Posted by Jonny View Post
    The answer is 42.
    No. because 0<x<1

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    Quote Originally Posted by Jonny View Post
    The answer is 42.
    Quote Originally Posted by Yautja_BR View Post
    No. because 0<x<1
    Hmm...Very puzzling. Is it 0.42 then? Or, as a wild guess, 1.18413465948497?

    Seriously though, I'll give it another attempt and hope to get an answer that's not impossible.
    Last edited by Day Tripper; 2012-06-29 at 06:43.

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    Yautja_BR (2012-06-29)

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    I made a trivial error, as I often do. It should be 0.8832035059135257.

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    Yautja_BR (2012-06-29)

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