If a regular polygon has 44 diagonals, how many sides does it have?
Show answer & explanation
Correct answer: D
Explanation
Number of diagonals = 44
According to the formula: Diagonals = n(n − 3) / 2
n(n − 3) / 2 = 44
⇒ n(n − 3) = 88
⇒ n² − 3n − 88 = 0
⇒ n² − 11n + 8n − 88 = 0
⇒ n(n − 11) + 8(n − 11) = 0
⇒ (n − 11)(n + 8) = 0
⇒ n = 11 (Positive value)
= 11 sides