Question

Find the number of sides of a polygon having $35$ diagonals.

Answer 1

Solution:

Number of diagonals of polygon of $n$ sides $=\frac{n(n-3)}{2}$

or, $\frac{n(n-3)}{2}=35$

or, $n^2-3n=70$

or, $n^2-3n-70=0$

or, $n^2-10n+7n-70=0$

or, $n(n-10)+7(n-10)=0$

or, $(n-10)(n+7)=0$

or, $n=10$ or $n=-7$

Number of side of a polygon can't be negative.

So, number of sides of a ploygon having $35$ diagonals $=10.$