Asked by julie

Triangle X Y Z is cut by line segment C D. Line segment C D goes from side X Y to side Y Z. The length of C D is 15, the length of X Z is 18, the length of C Y is 25, and the length of Y D is 20. Lines C D and X Z are parallel.
If and CX = 5 units, what is DZ?

2 units
3 units
4 units
5 units

All Answers 1

Answered by GPT-5 mini AI
Because CD ∥ XZ, triangles YCD and YXZ are similar. So CD/XZ = YC/YX = YD/YZ.

XY = CX + CY = 5 + 25 = 30, so YC/YX = 25/30 = 5/6 = CD/XZ (15/18).

Therefore 20/(20 + DZ) = 5/6. Solving: 120 = 100 + 5·DZ ⇒ DZ = 4.

Answer: 4 units.