AP EAMCET · Maths · Permutation Combination
A polygon has 54 diagonals. The number of sides of this polygon is
- A 12
- B 15
- C 16
- D 9
Answer & Solution
Correct Answer
(A) 12
Step-by-step Solution
Detailed explanation
Let number of sides of the polygon is \(n\), then number of diagonals is \(\begin{aligned} \frac{n(n-3)}{2} & =54 \quad \text{(given)} \\ \Rightarrow \quad n(n-3) & =108 \quad \Rightarrow n=12 \end{aligned}\)
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