Question

polygon has 35 diagonals, and then the number of its side's is__.

Answer 1

Number of diagonal of n sided polygon = ${}^n{C}_2-n$

Substitute the value of number of diagonals = 35

${}^n{C}_2-n=35\Rightarrow \frac{n!}{2!(n-2)!}-n=35$

$\Rightarrow n(n-1)-2n=70\Rightarrow n^2-3n=70$

$\Rightarrow n^2-3n-70=0\Rightarrow (n+7)(n-10)=0\Rightarrow n=10$