A polygon has 35 diagonals, then the number of its sides is

Question

Smart Achievers · Accepted Answer

(3)

$Number of diagonals = {}^{n}C_{2} - n = 35 given,$ $n is the number of sides.$

$\Rightarrow \frac{n (n - 1)}{2} - n = 35$ $\Rightarrow \frac{n (n - 3)}{2} = 35$ $\Rightarrow n (n - 3) = 70$

$\Rightarrow n (n - 3) = 10 \times 7$ $\Rightarrow n^{2} - 3 n - 10 \times 7 = 0$

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

$∴$ $n = 10$ $(As n + 7 \neq 0)$

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