SOLUTION: Triangle inequality Theorem, need to make a conclusion about AC AB+AC=5;AC+BC=4

Question 1200101: Triangle inequality Theorem, need to make a conclusion about AC
AB+AC=5;AC+BC=4
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
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Triangle inequality Theorem, need to make a conclusion about AC
AB + AC = 5; AC + BC = 4
~~~~~~~~~~~~~~~~~~~~~

We are given these two equalities

    AB + AC = 5    (1)

    AC + BC = 4    (2)


Subtract (2) from (1)  (both sides).  The terms "AC" will annihilate, so we will get

    AB - BC = 5 - 4 = 1.    (3)


Due to triangle inequalities,

    | AB - BC | < AC  for any triangle ABC.


So, from (3) we conclude that

    1 < AC,  or  AC > 1.


ANSWER.  From the given equalities, the triangle inequalities imply AC > 1.

Solved.

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