Question

If a polygon of $n$ sides has $275$ diagonals, then $n$is equal to

• A. $25$
• B. $35$
• C. $20$
• D. $15$

Answer 1

The correct option is A

$25$

Finding the value of :

Let, number of sides $=n$, number of vertex $=n$, number of lines $={}^{n}C_2$

Number of diagonals $={}^{n}C_2–n=\frac{n(n-3)}{2}$

$$\begin{gathered} \Rightarrow 275=\frac{n(n-3)}{2} \\ \Rightarrow n^2-3n=550 \\ \Rightarrow n^2–3n–550=0 \end{gathered}$$

Solving for $n$, we get;

$n=25,-22$

The number of sides cannot be negative. Therefore, $n=25$.

Hence, the correct option is (A).