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Let Tn be the number of all possible t...

Let `T_n` be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If `T_(n+1)-T_n=""10` , then the value of n is (1) 5 (2) 10 (3) 8 (4) 7

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To solve the problem, we need to determine the value of \( n \) such that the difference in the number of triangles formed by an \( n \)-sided polygon and an \( (n+1) \)-sided polygon equals 10. ### Step-by-step Solution: 1. **Understanding the Number of Triangles**: The number of triangles that can be formed by joining the vertices of an \( n \)-sided polygon is given by the combination formula \( T_n = \binom{n}{3} \). This is because a triangle requires 3 vertices. 2. **Formulating the Expression for \( T_{n+1} \)**: ...
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