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Math Help - finding lengths of this shape :/

  1. #1
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    finding lengths of this shape :/

    heya everyone

    ImageShack - Image Hosting :: problemfbp.jpg


    have been puzzling at this for over an hour now :/ tried using simutaneous equations



    20^2 = x^2 + (a+b)^2 - pithag..
    30^2 = y^2 + (a+b)^2 - pithag
    x / 8 = (a + b) / b - height/length ratios
    y / 8 = (a + b) / a - height/length ratios...

    where a and b is D split up into the smaller triangles...

    but solving these seems very tedious..anyone that can help?

    thanks in advance.


    oh btw the problem is solve X Y and D

    ps. the 8 is the length of the blue line. sorry its a bit sketchy
    edit2: math wrapped it lol.
    Last edited by miranlol; June 2nd 2009 at 07:21 AM.
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  2. #2
    MHF Contributor Amer's Avatar
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    this is your picture

    finding lengths of this shape :/-good.jpg



    - pithag..
    - pithag
    - height/length ratios
    - height/length ratios...

    where a and b is D split up into the smaller triangles...
    OK let d=a+b ..so b=d-a ok

    now you have

    400=x^2+d^2.......(1)

    900=y^2+d^2....(2)

    \frac{x}{8}=\frac{d}{d-a}...(3)

    \frac{y}{8}=\frac{d}{a}....(4)

    and from (3)

    a=\frac{d(x-8)}{x}

    sub this in equation (4)

    \frac{y}{8}=\frac{d}{\dfrac{d(x-8)}{x}}

    y(d(x-8))=8dx

    y=\frac{8x}{x-8}

    you continue it is now obvious right
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