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A polygon has 54 diagonals. The total number of distinct triangles that can be formed using its vertices is

A polygon has 54 diagonals. The total number of distinct triangles that can be formed using its vertices is

Grade:12

3 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
7 years ago
lets say polygon has n vertices then
number of diagonals is
\binom{n}{2} - n = 54
we get the quadratic
n^2-3n-108=0
whose roots are 12,-9
hence n=12
now total number of distinct triangle is given by
\binom{n}{3} = \binom{12}{3} = 220
manmath
49 Points
7 years ago
 
\binom{n}{3} = \binom{12}{3} = 220whose roots are 12,-9hence n=12now total number of distinct triangle is given byn^2-3n-108=0we get the quadratic\binom{n}{2} - n = 54 lets say polygon has n vertices thennumber of diagonals is
manmath
49 Points
7 years ago
 
\binom{n}{3} = \binom{12}{3} = 220whose roots are 12,-9hence n=12now total number of distinct triangle is given byn^2-3n-108=0we get the quadratic\binom{n}{2} - n = 54 hii, lets say polygon has n vertices thennumber of diagonals is

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