Question 8491: how many sides a convex polygan have if it has 35 distinct diagnals. Found 2 solutions by bonster, khwang:Answer by bonster(299) (Show Source):
You can put this solution on YOUR website! Assume it is a convex polygon with n sides
For each vertex v, there are n-3 possible diagonals passing through v.
(except the two adjacent vertices & v itself)
Since a diagonal (a line segment was counted twice from the two end
vertices), totally there are n(n-3)/2 = 35 diagonals.
Solve n(n-3)= 70, or n^2 - 3n - 70 = 0
Factoring (n-10)(n+7) = 0.
So n = 10 or n = -7(Illegal)
Answer : n = 10
Forget another terribly wrong answer,
Kenny
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