Q

# Please help! A convex polygon has 65 diagonals. The number of its sides is equal to -

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

• Option 1)

13

• Option 2)

10

• Option 3)

22

• Option 4)

11

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As learnt in concept

Geometrical Permutations -

The number of diagonals of n sided convex polygon is $^{n}c_{2}-n=\frac{n(n-3)}{2}$.

- wherein

Where n > 3

If number of sides =n

Number of diagonals = $\frac{n(n-3)}{2}= 65$

$n^{2}-3n-130=0$

$n^{2}-13n+10n-130=0$

$n= 13,-10$

Thus n =13

Option 1)

13

Correct option

Option 2)

10

Incorrect option

Option 3)

22

Incorrect option

Option 4)

11

Incorrect option

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