Question

Consider line segments of lengths 1, 2, 3, ..., 10, what is the number of triangles that can be formed from them?

• A. 20
• B. 30
• C. 40
• D. 50

Hint:

Remember the triangle inequality: the sum of the lengths of any two sides must be greater than the length of the third side.

Answer 1

The Correct Option is D

The total number of triangles that can be formed is determined by choosing three line segments at a time, and satisfying the triangle inequality.
The number of ways to choose three line segments from 10 is \( \binom{10}{3} = 120 \).
Out of these, 50 triangles satisfy the triangle inequality.