Magical Mathematics[Interesting Approach]> A polygon has 54 diagonals. The total num...

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

Radhakrishna Laishetty , 9 Years ago

Grade 12

3 Answers

Riddhish Bhalodia

Last Activity: 9 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

Last Activity: 9 Years ago

$\binom{n}{3} = \binom{12}{3} = 220$ whose roots are 12,-9hence n=12now total number of distinct triangle is given by $n^2-3n-108=0$ we get the quadratic $\binom{n}{2} - n = 54$ lets say polygon has n vertices thennumber of diagonals is

manmath

Last Activity: 9 Years ago

$\binom{n}{3} = \binom{12}{3} = 220$ whose roots are 12,-9hence n=12now total number of distinct triangle is given by $n^2-3n-108=0$ we get the quadratic $\binom{n}{2} - n = 54$ hii, lets say polygon has n vertices thennumber of diagonals is