SOLUTION: A polygon has 44 diagonals . Find the number of its sides

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Question 1138939: A polygon has 44 diagonals . Find the number of its sides
Answer by ikleyn(52787) About Me  (Show Source):
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The number of diagonals of any (convex) polygon is  %28n%2A%28n-3%29%29%2F2,

where "n" is the number of sides (vertices).


So, they ask you to find "n" from the equation


    %28n%2A%28n-3%29%29%2F2 = 44.


Simplify and solve for "n" :


    n*(n-3) = 44*2 = 88

    n^2 - 3n - 88 = 0

    (n-11)*(n+8) = 0


Of the two roots,  n= 11  and  n= -8,  only positive root n= 11 is meaningful solution to the problem.


ANSWER.  n = 11.  The number of sides and vertices is 11.

Solved.