Question

A polygon has 35 diagonals. How many sides does it have?

Answer 1

`d=35\\ d=(n(n-3))/(2)\\ d=(n(n-3))/(2)\\35=(n(n-3))/(2)\\ 70=n^2-3n\\ n^2-3n-70=0\\ n^2-10n+7n-70=0\\ n(n-10)+7(n-10)=0\\ (n+7)(n-10)=0\\ n=-7 \vee n=10\\\\ n=10`