Question

Which of the following possibilities will form a triangle?

Side = 12 cm, side = 5 cm, side = 6 cm
Side = 13 cm, side = 5 cm, side = 8 cm
Side = 12 cm, side = 5 cm, side = 8 cm
Side = 13 cm, side = 5 cm, side = 6 cm

Answer 1

Side = 12 cm, side = 5 cm, side = 8 cm

Explanation:

Side = 12 cm, side = 5 cm, side = 8 cm

Answer 2

Side = 12 cm, side = 5 cm, side = 8 cm

Explanation:

In order to form a triangle with non-zero area, the sum of the shortest two sides must exceed the longest side.

This will be the case for {5, 8, 12}, but not for any of the others.

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The side lengths {5, 8, 13} will form a triangle with zero area. This is acceptable according to one version of the triangle inequality (a+b≥c) but not according to the other version (a+b>c). Since you are apparently expected to find one "right answer", we assume the answer you want is the one shown above.