The sets of side lengths that can produce a triangle are
The triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
That is, in a given triangle of sides a, b and c,
a + b ≥ c
Analysing the sets of the side lengths given,
In triangle 2 cm, 7 cm, and 6 cm,
2 + 6 = 8,
Therefore 8cm which is greater than the third side being 7cm makes this side lengths possible to produce a triangle.
In triangle 2 m, 5 m, and 7 m,
2 + 5 = 7
Addition of both sides of the triangle is equal to the third side being 7m.
In triangle 6 ft, 6 ft, and 12 ft,
6 + 6 = 12
Addition of both sides of the triangle is equal to the third side being 12ft
Therefore the sets of side lengths could produce a triangle are
2 cm, 7 cm, and 6 cm
2 m, 5 m, and 7 m
6 ft, 6 ft, and 12 ft
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