JEE Mains · Maths · STD 11 - 6. permutation and combination
If in a regular polygon the number of diagonals is \(54\), then the number of sides of this polygon is
- A \(12\)
- B \(6\)
- C \(10\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(12\)
Step-by-step Solution
Detailed explanation
Number of diagonal \(=54\) \( \Rightarrow \frac{{n(n - 3)}}{2} = 54\) \( \Rightarrow {n^2} - 3n - 108 = 0\) \( \Rightarrow {n^2} - 12n + 9n - 108\) \( = 0\) \( \Rightarrow n(n - 12) + 9(n - 12) = 0\) \( \Rightarrow n - 12, - 9 \Rightarrow n = 12\,(\because \,n \ne - 9)\)
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