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Math Help - Concerning the altitude of an equilateral triangle

  1. #1
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    Concerning the altitude of an equilateral triangle

    I appologise if this is the wrong forum. I figured triangles are trigonometry.

    Are there any equilateral triangles where both h and a are integers?
    Concerning the altitude of an equilateral triangle-triangle-equilateral-001.gif
    I found this formula on the internet.

    h = (1/2) * √3 * a

    Is there any way to re-arrange it to get rid of the square root?

    I'm trying to write a program to answer my original question but it would round off a value for the square root which would make it impossible to find a match. Sorry if this is really basic, I left school a long time ago.
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  2. #2
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    Re: Concerning the altitude of an equilateral triangle

    Quote Originally Posted by blis View Post
    I appologise if this is the wrong forum. I figured triangles are trigonometry.
    Are there any equilateral triangles where both h and a are integers?
    Click image for larger version. 

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    I found this formula on the internet.
    h = (1/2) * √3 * a
    Is there any way to re-arrange it to get rid of the square root?
    \frac{4h^2}{a^2}=3

    But that is no better. Is it?
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  3. #3
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    Re: Concerning the altitude of an equilateral triangle

    I think that will work actually. Thank you.

    I can get it to keep trying different integers for a and h until it equals 3(if ever)
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    Re: Concerning the altitude of an equilateral triangle

    Quote Originally Posted by blis View Post
    I can get it to keep trying different integers for a and h until it equals 3(if ever)
    Let this be a lesson to everyone.
    Always post what you mean to ask in the first place.

    You never find integer solutions for a & h.

    In order for \frac{4h^2}{a^2}=3 we must have a=2\cdot 3^j~\&~h=3^k.

    In effect, 3^{2k-2j}=3. But that is impossible.
    Last edited by Plato; August 22nd 2011 at 02:58 AM.
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    Re: Concerning the altitude of an equilateral triangle

    Most of that goes over my head but to hear that it is indeed impossible saves me a lot of time.

    Thanks.

    You've inspired me to try and learn more about maths.
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