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COMEDK · Maths · 4. Permutation Combination

A polygon of n sides has 90 diagonals, then n is equal to

  1. A 20
  2. B \(-\)14
  3. C 21
  4. D 15
Verified Solution

Answer & Solution

Correct Answer

(D) 15

Step-by-step Solution

Detailed explanation

The formula for number of diagonals in a polygon of \(n\) sides is \(D = \dfrac{n(n-3)}{2}\) Setting \(D = 90\): \(\dfrac{n(n-3)}{2} = 90\) \(n^2 - 3n - 180 = 0\) \((n-15)(n+12) = 0\) \(n = 15\) or \(n = -12\) Since \(n\) must be a positive integer, \(n = 15\).