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Math Help - Geometry

  1. #1
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    Question Geometry

    How many triangles are there in a polygon, if the polygon has 44 diagonals?
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  2. #2
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    Quote Originally Posted by sureshrju View Post
    How many triangles are there in a polygon, if the polygon has 44 diagonals?
    Try to draw out the diagonals for the first couple of polygons. See if you can deduce a pattern in the number of triangles.
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  3. #3
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    Hello Arcketer,

    Draw the first couple of polygon in the sense? I can not understand
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  4. #4
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    Hello, sureshrju!

    Please check the wording of the problem . . .


    How many triangles are there in a polygon, if the polygon has 44 diagonals?
    A convex polygon with n sides has: . \frac{n(n-3)}{2} diagonals.

    . . But . \frac{n(n-3)}{2} \:=\:44 .has no integral solutions. . . . . . wrong!

    I did some very bad algebra . . . sorry!


    Last edited by Soroban; March 6th 2010 at 09:07 AM.
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  5. #5
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    Hi Saroban,

    There is any polygon of concave? My friend ask this question to me, So i can not check the question again, i asked him about the question he said it is the correct one.

    n(n-3)/2=44
    n(n-3)=88
    n^2-3n=88
    n^2-3n-88=0
    Then, (n+8)(n-11)=0
    n=-8 or n=11
    Since n denotes side, it can not be negative. So, n=11.
    So, it is a polygon of 11 sides.

    Can you please help me in finding out the number of triangles in the 11 sided polygon?
    Last edited by sureshrju; March 6th 2010 at 07:41 AM.
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  6. #6
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    In fact \frac{n(n-3)}{2}=44 does have integral solutions: 11~\&~-8.
    Thus we have 11 vertices.
    The number of triangles on 11 non-collinear points is \binom{11}{3}.
    If you are asking for the total number of triangle formed by the diagonals and/or sides that is a different matter.
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  7. #7
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    Hello Plato,

    Is there any method to find the number of triangles formed by the sides and diagonals?
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  8. #8
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    Quote Originally Posted by sureshrju View Post
    Hello Plato,
    Is there any method to find the number of triangles formed by the sides and diagonals?
    That is the number I gave you: \binom{11}{3}.
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