COMEDK · Maths · 4. Permutation Combination
If a \(n\)-sided polygon has total 54 diagonal then the value of \(n\) is
- A 10
- B 11
- C 12
- D 13
Answer & Solution
Correct Answer
(C) 12
Step-by-step Solution
Detailed explanation
\(\because\) Number of diagonal in \(n\)-sided polygon \(\begin{array}{ll} & =\frac{n(n-3)}{2} \\ \Rightarrow \quad & \frac{n(n-3)}{2}=54 \\ & n^2-3 n=108 \\ & n^2-3 n-108=0 \\ \therefore \quad & n=12 \text { or } n=-9 \end{array}\)
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