If the number of diagonals in regular polygon is 44, then the number of sides in the polygon will be ________.

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DFCCIL Executive CBT1 Electrical 25 Aug 2023 Shift 2 Official Paper
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  1. 12
  2. 9
  3. 10
  4. 11

Answer (Detailed Solution Below)

Option 4 : 11
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Detailed Solution

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Given:

The number of diagonals in a regular polygon = 44

Formula used:

The number of diagonals in a polygon with n sides is given by:

\(\dfrac{n(n-3)}{2} = 44\)

Calculation:

\(\dfrac{n(n-3)}{2} = 44\)

\(n(n-3) = 88\)

\(n^2 - 3n - 88 = 0\)

⇒ \(n^2 - 11n + 8n - 88 = 0\)

⇒ n(n - 11) + 8(n - 11) = 0

⇒ (n - 11) (n + 8) = 0

⇒ n = 11 and - 8

Considering the positive value:

⇒ n = 11.

∴ The correct answer is option (4).

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