# Which three lengths could be the lengths of the sides of a triangle?

**Solution:**

Let us see the nature of the sides of a triangle using the triangle inequality theorem.

The two conditions of the sides of a triangle are:

- The sum of the two sides is always greater than the third side.
- a + b > c
- b + c > a
- c + a > b

- The difference between the two sides is less than the third side.
- |a - b| < c
- |b - c| < a
- |c - a| < b

Hence, three lengths could be the lengths of the sides of a triangle if and only if the sum of two sides is always greater than the third side and the difference of the two sides is less than the third side.

## Which three lengths could be the lengths of the sides of a triangle?

**Summary:**

(a, b, c) can be the sides of a triangle if and only if the sum of two sides is always greater than the third side and the difference of the two sides is less than the third side.

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