Question

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What can you conclude about AC in ABC?
AB = 6; BC+AC=18

Answer 1

Answer:

Finally, substitute AB = 6 and BC = 18 - 2AC in

AB + AC > BC 3rd Triangle Inequality condition

6 + AC > 18 - 2AC

   -12 > -3AC

     4 < AC

    AC > 4

So putting all three results together

AC < 12, AC < 8, and AC > 4

Since AC is less than 8, it's automatically less than 12,

so we can dispense with AC < 12.  So we have:

AC < 8 and AC > 4  which can be combined and written as

   4 < AC < 8    [that is, AC is between 4 and 8]