Answer:
[tex]22 > x > 10[/tex]
[tex]10 < x < 22[/tex]
Step-by-step explanation:
Given
[tex]Side\ 1 = 6[/tex]
[tex]Side\ 2 = 16[/tex]
Required
Determine the inequality that represents the third side
Represent the third side with x.
For the triangle to be true, two of the following condition must be true.
[tex]6 + 16 > x[/tex]
[tex]6 + x > 16[/tex]
[tex]16 + x > 6[/tex]
[tex]6 + 16 > x[/tex]
[tex]22>x[/tex] -- True
[tex]6 + x > 16[/tex]
[tex]x > 16 - 6[/tex]
[tex]x > 10[/tex] -- True
[tex]16 + x > 6[/tex]
[tex]x > 6 - 16[/tex]
[tex]x > -10[/tex] --- False; Because, x can't be negative.
So, we have:
[tex]22>x[/tex] and [tex]x > 10[/tex]
This can be combined to give:
[tex]22 > x > 10[/tex]
or
[tex]10 < x < 22[/tex]
