Question

Help me understand this problem

Answer 1

It ΔABC and ΔXYZ are similar, then the sides of the triangles are in proportion.

`(AB)/(XY)=(BC)/(YZ)=(AC)/(XZ)`

We have BC = 8, AC = 7, Y = 28, XZ = 49 and YZ = 56. Substitute:

`(AB)/(XY)=(BC)/(YZ)\to(AB)/(28)=(8)/(56)\qquad\text{cross multiply}\\\\56AB=(8)(28)\qquad\text{divide both sides by 56}\\\\AB=(224)/(56)\\\\\boxed{AB=4}`