# Answer to Question #4059 in Geometry for Jessica

Question #4059

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

Expert's answer

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

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

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