An angle bisector of a triangle divides the opposite side of the triangles into segments 6cm and 4cm long. a second side of triangle is 7.4 cm long. find the longest and shortest possible lengths of the thrid side of the triangle

From the angle bisector theorem
we can first assume the third side is x, therefore
7.4/6 = x/4
    x = 7.4 × 4/6
     x =  4.93 cm
We can also use, 
7.4/4 = x/6
      x = 7.4 ×6/4
      x = 11.1 cm
Therefore, the shortest length of the third side is 4.93 cm while the longest length is 11. 1 cm

The first one is 2/3the second is 1/160the third is 4/125