Question

Two sides of a triangle have lengths 5 and 12. Which inequalities represent the possible lengths for the third side, x?

Answer 1

x < 17 is the inequality that represents the possible length of the third side.

Answer 2

`x> 7`

`x< 17`

Explanation:

we know that

The Triangle Inequality Theorem states that the sum of any
`2` sides of a triangle must be greater than the measure of the third side

Let

x------> the length of the third side

a)
`x+5 > 12` ------>
`x> 7`

b)
`12+5 > x` ---->
`17 > x` ------>
`x< 17`

The possible lengths for the third side is the interval------>
`(7,17)`