Use the triangles to find the missing length of segment TU.

Option C is the correct answer.

Step-by-step explanation:

Triangle STU is similar to triangle SVW. This means that the ratio of the length of each side of ∆STU to the length of the corresponding side of ∆ SVW is constant. Therefore,

ST/SV = TU/VW = SU/SW

SV = 12 + 18 = 30 in

Therefore,

12/30 = TU/40

Cross multiplying, it becomes

TU × 30 = 12 × 40

30TU = 480

Dividing the left hand side and the right hand side of the equation by 30, it becomes

30TU/30 = 480/30

TU = 16