TS EAMCET · Maths · Permutation Combination
The number of diagonals of a polygon is 35 . If A, B are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having \(\mathrm{AB}\) as one of its sides is
- A \(1\)
- B \(8\)
- C \(10\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(8\)
Step-by-step Solution
Detailed explanation
Number of diagonals \(={ }^n \mathrm{C}_2-n\) \[ \begin{aligned} & =\frac{n(n-1)}{2}-n=35 \\ & \Rightarrow n^2-n-2 n=35 \times 2 \Rightarrow n^2-3 n-70=0 \\ & \Rightarrow(n-10)(n+7)=0 ; \therefore n=10 \end{aligned} \] To form triangle we need 3 vertices out of which 2 are \(A\)…
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