Question : A polygon has 54 diagonals. The number of sides in the polygon is:
Option 1: 7
Option 2: 9
Option 3: 12
Option 4: 15
Answer (1)
24th Jan, 2024
Correct Answer: 12
Solution :
Let the number of sides be $n$.
Then, number of diagonals of the polygon = $\frac{n(n-3)}{2}$
So, $\frac{n(n-3)}{2}=54$
⇒ $n^2-3n=108$
⇒ $n^2-3n-108=0$
⇒ $(n-12)(n+9)=0$
⇒ $n$ =12, the negative value is rejected.
Hence, the correct answer is 12.
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