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  1. #1
    Junior Member wpcp15's Avatar
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    Unhappy Geometry Help

    In Triangle ABC, segmentS CM, BP, and AN are medians

    If CM=3X+6 and CE=x+12, find the value of x. Being that e is the centroid.
    I know that from the vertex to the centroid is 2/3 of the entire median, but i cant figure out what x equals
    I think the value of x equals 18, but im not sure


    Also, I need help answering
    If EN= X-5 and AE=X+17, find the value of AN.
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  2. #2
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    Quote Originally Posted by wpcp15
    In Triangle ABC, segmentS CM, BP, and AN are medians

    If CM=3X+6 and CE=x+12, find the value of x. Being that e is the centroid.
    I know that from the vertex to the centroid is 2/3 of the entire median, but i cant figure out what x equals
    I think the value of x equals 18, but im not sure


    Also, I need help answering
    If EN= X-5 and AE=X+17, find the value of AN.
    Since, CM is the entire median and CEis the centroid then just like you said.
    \frac{2}{3}CM=CE
    But, CM=3x+6 and CE=x+12
    Thus, (substitute)
    \frac{2}{3}(3x+6)=x+12
    Now, open paranthese,
    2x+4=x+12
    Subtract x from both sides,
    x+4=12
    Subtract 8 from both sides,
    x=8
    Thus, CM=30 and CE=20.
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  3. #3
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    For the second answer.
    Remember that the ratio from the vertex to the centriod to to the remaining part of the median is 2:1.
    Thus,
    \frac{AE}{EN}=\frac{2}{1}
    But, AE=x+17 and EN=x-5
    Thus, (substitute)
    \frac{x+17}{x-5}=\frac{2}{1}
    Cross multiply,
    (x+17)1=2(x-5)
    Open parantheses,
    x+17=2x-10
    Subtract x from both sides,
    17=x-10
    Add 10 to both sides,
    27=x
    Thus, AE=44 and EN=22.

    Q.E.D.
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  4. #4
    Junior Member wpcp15's Avatar
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    Thank you
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  5. #5
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    Welcome.
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