A convex polygon has $65$ diagonals. The number of its sides is equal to

13

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Solution

The correct option is A $13$
Let number of sides be n

$∴ \frac{n (n - 3)}{2} = 65$

$∴ n (n - 3) = 130$

$∴ n^{2} + 3 n - 130 = 0$

$∴ n^{2} + 10 n - 13 n - 130 =$

$∴ (n - 13) (n + 10) = 0$

Since there could be no polygon having $- 10$ side

$∴ n = 13$

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A convex polygon has 65 diagonals. The number of its sides is equal to

The correct option is A 13Let number of sides be n∴n(n−3)2=65∴n(n−3)=130∴n2+3n−130=0∴n2+10n−13n−130=∴(n−13)(n+10)=0Since there could be no polygon having −10 side ∴n=13

A convex polygon has $65$ diagonals. The number of its sides is equal to

The correct option is A $13$
Let number of sides be n

$∴ \frac{n (n - 3)}{2} = 65$

$∴ n (n - 3) = 130$

$∴ n^{2} + 3 n - 130 = 0$

$∴ n^{2} + 10 n - 13 n - 130 =$

$∴ (n - 13) (n + 10) = 0$

Since there could be no polygon having $- 10$ side

$∴ n = 13$