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

Last updated date: 17th Mar 2023
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Hint- The Number of diagonals are given here .So, we use the formula of finding the Number of diagonals of a polygon having n sides $= \dfrac{{n\left( {n - 3} \right)}}{2}$
As we know that the number of diagonals of polygon having n sides $= \dfrac{{n\left( {n - 3} \right)}}{2}$
$\therefore 35 = \dfrac{{n\left( {n - 3} \right)}}{2}$
$\begin{gathered} \Rightarrow {n^2} - 3n = 70 \\ \Rightarrow {n^2} - 3n - 70 = 0 \\ \end{gathered}$
$\begin{gathered} \Rightarrow {n^2} - 10n + 7n - 70 = 0 \\ \Rightarrow n\left( {n - 10} \right) + 7\left( {n - 10} \right) = 0 \\ \Rightarrow \left( {n - 10} \right)\left( {n + 7} \right) = 0 \\ \Rightarrow \left( {n - 10} \right) = 0{\text{ \& }}\left( {n + 7} \right) = 0 \\ \therefore n = 10,{\text{ - 7}} \\ \end{gathered}$