Question

Consider a convex polygon having $35$ diagonals, then find the number of sides of the polygon

• A. $10$
• B. $60$
• C. $120$
• D. $210$

Answer 1

The correct option is A $10$

For polygon with $n$ number os sides, the number of diagonals are $\frac{n}{2}(n-3)$

So,

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

$\Rightarrow$ $n(n-3)=70$

$\Rightarrow$ $n^2-3n-70=0$

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

$\Rightarrow$ $n(n-10)+7(n-10)=0$

$\Rightarrow$ $(n-10)(n+3)=0$

$\Rightarrow$ $n-10=0$ and $n+7=0$

$\Rightarrow$ $n=10$ or $n=-7$

Number of sides cannot be negative so $-7$ is not an answer.

$\Rightarrow$ So, the number of sides of the polygon is $10.$