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TS EAMCET · Maths · Permutation Combination

A polygon has 54 diagonals. Then, the number of its sides is

  1. A 7
  2. B 9
  3. C 10
  4. D 12
Verified Solution

Answer & Solution

Correct Answer

(D) 12

Step-by-step Solution

Detailed explanation

Number of diagonals in polygon \(=54\) Let the number of sides in polygon \(=n\) Then, The number of diagonal in any polygon \(=\frac{n(n-3)}{2}\) \(54=\frac{n(n-3)}{2}\) \(n^2-3 n=108\) \(n^2-3 n-108=0\) \(n^2-12 n+9 n-108=0\) \(n(n-12)+9(n-12)=0\) \((n+9)(n-12)=0\) \(n=-9\) or…