Answer to Question #4059 in Geometry for Jessica

Question

In the diagram, points V, W, X, Y, and Z are collinear, VZ=52, XZ=20, and WX=XY=YZ. Find the length of WX

Answer 1

Since WX = XY = YZ, assume they are all of R length, hence
VX - WX = VW :: 32 -R = VW
3R + VW = 52 :: We have two equations and two unknowns, so we can solve the system for R and VW
R = 32 -VW :: 3(32-VW) + VW =52
96 -3VW + VW = 52
96 - 2VW = 52
2VW = 96 - 52
2VW = 44
VW = 22
R = 32- VW = 32 -22 = 10
Answer: VW = 22, WX = XY = YZ = 10, WY = 20, WZ = 30, VY = 42