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An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5cm long. A second side of the triangle is 6.9cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of centimeter.

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Segments either side of an angle bisector are proportional.

The longest the third side (x) could be is
  6/5 = x/6.9
  x = 6/5*6.9 = 8.28

The shortest the third side could be is
  5/6 = x/6.9
  x = 5/6*6.9 = 5.75

The longest and shortest possible lengths for the third side are ...
  8.3 cm and 5.8 cm.

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