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Math Help - another triangle area proof

  1. #1
    Member jacs's Avatar
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    another triangle area proof

    a triangle ABC is such that AB = 12 and AC = 8. X is the midpoint of the base BC. If the area of the triangle is 72, what is the length of the perpendicular from X to AB and to AC?


    thanks
    jacs
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jacs
    a triangle ABC is such that AB = 12 and AC = 8. X is the midpoint of the base BC. If the area of the triangle is 72, what is the length of the perpendicular from X to AB and to AC?


    thanks
    jacs
    Drop a perp from C onto AB, call its length u, then Area(ABC)=12*u/2=72,
    so u=12. Then the length of the perp from X onto AB is u/2=6 (similar
    triangles).

    Drop a perp from B onto AC, call its length v, then Area(ABC)=8.v/2=72,
    so v=18. Then the length of the perp from X onto AC is v/2=9 (similar
    triangles).

    RonL
    Last edited by CaptainBlack; April 27th 2006 at 04:17 AM.
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  3. #3
    Member jacs's Avatar
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    thanks a lot, that works beautifully, appreciate your help.
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