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

Answer:

$x> 7$

$x< 17$

Step-by-step 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------> $(7,17)$