Question

Identify the lengths of QS and SR

Answer 1

The bisector of an angle of a triangle divides the opposite side into segments that are proportional to the adjacent sides  ⇒

10/12 = (3x+2)/(5x-0.4)
10(5x-0.4) = 12(3x+2)
50x - 4 = 36x + 24
50x - 36x = 24 + 4
14x = 28
x = 28/14
x = 2

QS = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 
SR = 5x - 0.4 = 5*2 - 0.4 = 10 - 0.4 = 9.6

Answer is QS=8, SR=9.6