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Math Help - Find the area

  1. #1
    Newbie PxEckx's Avatar
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    Question Find the area

    Good Afternoon!!!

    Please, can you help me with it?




    Where AB = 5, AD = 3, CE = 1. The area of the triangle BCF is?

    I started making some analogy between similar triangles:

    First: between ABF and CEF

    But Im not sure...

    What can I do now?!
    Attached Thumbnails Attached Thumbnails Find the area-find_area.jpg  
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  2. #2
    MHF Contributor
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    Quote Originally Posted by PxEckx View Post
    Good Afternoon!!!

    Please, can you help me with it?



    Where AB = 5, AD = 3, CE = 1. The area of the triangle BCF is?

    I started making some analogy between similar triangles:

    First: between ABF and CEF

    But Im not sure...

    What can I do now?!
    Yes, you can continue along that route if you like.
    Triangles ABF and CEF are similar. ABF is CEF magnified.

    The base of ABF is 5 and the base of CEF is 1.
    This means that the perpendicular height of CEF is one-fifth of the perpendicular height of ABF,
    since the linear measurements of ABF are 5 times those of CEF.

    Hence you must divide AD or BC into 6 equal subdivisions.
    Then you have the base and perpendicular height of CEF,
    so you can find it's area.

    Can you finish ?

    OOps!!! sorry, that's ECF not BCF.

    However, you then only need subtract the area of ECF from ECB which is easy.
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  3. #3
    Newbie PxEckx's Avatar
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    Ahhhh! Now I undertood!

    I made the 'divison' as you said (but of the BCF!) , and I fond the height!

    h=\displaystyle{\frac{5}{6}}

    Then I just calculate the area!

    \displaystyle{\frac{BC.h}{2} = \displaystyle{\frac{5}{4}

    Thanx!!!!
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  4. #4
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    Well done!

    Quite clever...
    You found 5/6 of EC.
    Last edited by Archie Meade; August 23rd 2010 at 05:21 PM.
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