Question
Download Solution PDFIf the number of diagonals in regular polygon is 44, then the number of sides in the polygon will be ________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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