Question

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


1 cm, 2 cm, 3 cm


3 in., 3 in., 7 in.


4 ft, 8 ft, 12 ft


5 cm, 7 cm, 9 cm

Answer 1

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

- 1, 2, 3: 1 + 2 = 3 → not > 3, so no (degenerate).
- 3, 3, 7: 3 + 3 = 6 < 7 → no.
- 4, 8, 12: 4 + 8 = 12 → not > 12, so no (degenerate).
- 5, 7, 9: 5 + 7 = 12 > 9, 5 + 9 = 14 > 7, 7 + 9 = 16 > 5 → yes.

Thus only 5 cm, 7 cm, 9 cm can form a (nondegenerate) triangle.