Question

A triangle has two sides with lengths 5 cm and 8 cm. Which statement could be true about the triangle? Choose all that apply A: The third side could be 13 cm long. B: The third side could be less than 5 cm long. C: The triangle could be isosceles. D: The sum of all side lengths could be 15 cm. E: The sum of all side lengths could be 23 cm.

Answer 1

The Triangle Inequality Theorem states that any side of a triangle must be shorter than the other two sides added together.

When the three sides are a, b and c, we can write:

Therefore, the third side must be less than:

`\begin{gathered} c<5+8 \\ c<13 \end{gathered}`

Using the second inequality, we can have:

`\begin{gathered} b-ab-a \\ c>8-5 \\ c>3 \end{gathered}`

Therefore, the third side must be between the inequality:

[tex]3Hence, the following options are true:

OPTION B

OPTION C

OPTION E