Question

I need to know if I got number 13 right

Answer 1

The given side lengths are 38mm, 45mm, and 82mm.

It is required to use inequalities to prove if the side lengths could form a triangle.

Recall the Triangle Inequality Theorem: The Triangle Inequality Theorem states that the sum of the measures of two sides of a triangle is greater than the measure of the third side.

Check the inequality:

`\begin{gathered} 38+45>82\Rightarrow83>82-True \\ 38+82>45\Rightarrow120>45-True \\ 45+82>38\Rightarrow127>38-True \end{gathered}`

Hence, the side lengths can form a triangle.

The required inequality is 38+45>82.