Question

Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.

Answer 1

The side lengths given form a triangle

Step-by-step explanation:

Let the lengths of the sides of the triangle be "a", "b" and "c"

For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:

`\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}`

Given the sides of the triangle as 34km, 27km, and 58km

Let a = 34km, b = 27km and c = 58km

Substituting these values in the expression above to check if it is true:

`\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}`

Since the inequality expression supports the theorem above, hence the side lengths given form a triangle