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Let Tₙ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_(n+1) - Tₙ = 10 then the value of n is -

1. 10
2. 8
3. 7
4. 5

Correct answer: 5

Solution

The number of triangles that can be formed from the vertices of an n-sided polygon is given by the combination formula C(n, 3). The difference T_(n+1) - Tₙ represents the additional triangles formed when adding one more vertex, which can connect to any two of the existing n vertices, resulting in nC2 new triangles. Setting this equal to 10 allows us to solve for n, leading to the conclusion that n must be 5.

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