Question

7. Each set of numbers below represents the lengths of three line segments.

Which set represents line segments that could be connected to form a triangle:

A. (1, 2, 3)
B. (3, 4, 5)
C. (1, 10, 100)
D. (1, 2, 5)
E. (1, 3, 4)
F. (1, 20, 100)

Please don't just give a letter choice as an answer. There are more questions like this one and I'd like to understand how to do it : )

Answer 1

B: (3, 4, 5)

Explanation:

You want to know which segment lengths could be used to form a triangle.

Triangle inequality

The triangle inequality requires the sum of the two short sides of a triangle exceed the length of the longest side.

A: 1+2 = 3 . . . not a triangle

B: 3+4 > 5 . . . forms a triangle

C: 1+10 < 100 . . . not a triangle

D: 1+2 < 5 . . . not a triangle

E: 1+3 = 4 . . . not a triangle

F: 1+20 < 100 . . . not a triangle

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Additional comment

The above expression of the triangle inequality seems to be the one most commonly used in algebra and geometry courses.

The triangle inequality can also be seen to be expressed as ...

a + b ≥ c . . . . . . where a, b, c are side lengths in any order

The "equal to" case allows triangles of zero height. (They look like a line segment.) Using that formulation, triples A and E in your answer list will also be considered to form a "triangle."