MHT CET · Maths · Permutation Combination
A polygon has 44 diagonals. Then the number of sides of the polygon are
- A 11
- B 12
- C 10
- D 13
Answer & Solution
Correct Answer
(A) 11
Step-by-step Solution
Detailed explanation
Number of diagonals of ' \(n\) ' sided polygons \(={ }^n C_2-n\)
\(\therefore{ }^n C_2-n=44 \)
\(\frac{n !}{2 !(n-2) !}-n=44 \Rightarrow n(n-1)-2 n=88 \)
\(\therefore n^2-3 n-88=0 \Rightarrow(n-11)(n+8)=0 \)
\(\Rightarrow n=11 \ldots[n \in N]\)
\(\therefore{ }^n C_2-n=44 \)
\(\frac{n !}{2 !(n-2) !}-n=44 \Rightarrow n(n-1)-2 n=88 \)
\(\therefore n^2-3 n-88=0 \Rightarrow(n-11)(n+8)=0 \)
\(\Rightarrow n=11 \ldots[n \in N]\)
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