Given six non-parallel line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that can be formed by these lines is _____.

- 7

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- 6

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- 5

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Solution

The correct option is A
- 7

Total No. of triangles = $^{6} C_{3}$

To form a triangle sum of two sides of triangle should be greater than third side.

2+ 3 is NOT greater than 5, 6 and 7 units

2 + 4 is NOT greater than 6 and 7 units

2 + 5 is NOT greater than 7 units

4 + 3 is NOT greater than 7 units

We see that there are seven-cases for which sum of two sides of triangle is not greater than third side.

So, No. of triangles = $^{6} C_{3}$ - 7

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