Question

Determine if each set of side lengths could be used to create a triangle. *Explain your reasoning.*

a. 2 cm, 6 cm, 7 cm
b. 3 cm, 3 cm, 3 cm
c. 5 cm, 7 cm, 12 cm

Answer 1

See below

Explanation:

By the Triangle Inequality Theorem, if given side lengths
`a`,
`b`, and
`c`, where
`c` is the longest side, then
`a+b\geq c`

Problem A

This set of side lengths creates a triangle since
`2+6\geq7`

Problem B

This set of side lengths creates a triangle since
`3+3\geq 3`, which is known as an equilateral triangle since all of its side lengths are equal to each other

Problem C

This set of side lengths creates a triangle since
`5+7\geq 12`