SOLUTION: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In triangle ABC, BC = 4 and AC = 8

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Question 896909: The sum of the lengths of any two sides of a triangle is greater than
the length of the third side. In triangle ABC, BC = 4 and AC = 8 - AB. What can
you conclude about AB?
Answer : 2 < AB < 6
Please show me work/explanation to get to this answer, thank you
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The sum of the lengths of any two sides of a triangle is greater than
the length of the third side.
In triangle ABC, BC = 4 and AC = 8-AB .
What can you conclude about AB?
------
Using the fact stated above you get:
BC + AC > AB
4 + 8-AB > AB
Adding AB to both sides you get:
12 > 2*AB
Then AB < 6
----
Also 4 + AB > 8-AB
Then 2AB > 4
AB > 2
----
Putting those together you get:
2 < AB < 6
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Cheers,
Stan H.
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SOLUTION: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In triangle ABC, BC = 4 and AC = 8 - AB. What can you conclude about AB? An