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Combination with Restrictions

If in a regul...

Question

If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is

A

12

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B

10

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C

6

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D

9

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Solution

The correct option is C 12
We know polygon having $n$ side will have $\frac{n (n - 3)}{2}$ diagonals
$\Rightarrow \frac{n (n - 3)}{2} = 54 \Rightarrow n (n - 3) = 108 \Rightarrow n = 12$

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