A polygon has 35 diagonals. Find the number of its sides.

1.	A polygon has 35 diagonals. Find the number of its sides.
Answer» Let n be the number of sides of a polygon and D be the number of diagonals of that polygon We know that, D = \(n_{c_2}\) - n = \(\frac{n(n-3)}{2}\) ∴ 35 = \(\frac{n^2-3n}{2}\) ⇒ n² − 3n − 70 = 0 ⇒ (n − 10)(n + 7) = 0 ⇒ n = 10, −7 Since, sides cannot be negative, therefore n = 10. Hence, polygon is a decagon.

Answer»

Let n be the number of sides of a polygon and D be the number of diagonals of that polygon

We know that, D = \(n_{c_2}\) - n = \(\frac{n(n-3)}{2}\)

∴ 35 = \(\frac{n^2-3n}{2}\)

⇒ n² − 3n − 70 = 0

⇒ (n − 10)(n + 7) = 0

⇒ n = 10, −7

Since, sides cannot be negative, therefore n = 10.

Hence, polygon is a decagon.

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