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Find the number of sides of a polygon which has 14 diagonals. |
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Answer» Number of diagonals of a polygon of n sides = \(\frac { n(n-1) }{ 2 }\) – n ⇒ 14 = \(\frac { n(n-1) }{ 2 }\) – n ⇒ 28 = n2 – n – 2n ⇒ n2 – 3n – 28 = 0 ⇒ n2 – 7n + 4n – 28 = 0 ⇒ n(n – 7) + 4(n – 7) = 0 ⇒ (n – 7) (n + 4) = 0 ⇒ n = 7 |
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