Given, 5 line segments of lengths 2,3,4,5,6 units. Then, the number of triangles that can be formed by joining these segments is

Step-by-step solution

To form a triangle, 3 line segments are needed. We can choose 3 line segment from 5 line segments in 5 3 ways. We know that in a triangle, sum of two sides is always greater than third side. So, line segments of length (2,3,5),(2,3,6) and (2,4,6) do not form any triangle. Total number of triangles formed = 5 3 -3 .