COMEDK · Maths · 4. Permutation Combination
If a polygon of \(n\) sides 275 diagonals, then \(n\) is equal to
- A \(25\)
- B 35
- C 20
- D 15
Answer & Solution
Correct Answer
(A) \(25\)
Step-by-step Solution
Detailed explanation
A polygon of \(n\) sides has number of diagonals \[ =\frac{n(n-3)}{2}=275 \quad\text{[given]} \] \(\Rightarrow \quad n^{2}-3 n-550=0\) \(\Rightarrow \quad(n-25)(n+22)=0\) \(\therefore \quad n=25 \quad[n \neq-22]\)
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