Answer:
y = 3, TU = 6
Step-by-step explanation:
SU is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is
[tex]\frac{SV}{ST}[/tex] = [tex]\frac{VU}{TU}[/tex] , substitute values
[tex]\frac{24}{4y-2}[/tex] = [tex]\frac{14.4}{2y}[/tex] ( cross- multiply )
14.4(4y - 2) = 48y
57.6y - 28.8 = 48y ( subtract 48y from both sides )
9.6y - 28.8 = 0 ( add 28.8 to both sides )
9.6y = 28.8 ( divide both sides by 9.6 )
y = 3
Then
TU = 2y = 2 × 3 = 6
