Question

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

Answer 1

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