Geometry help

1)

△ABC ~ △HGF    and    AB = 72    and    BC = 48    and    HG = 12

 

GF / BC  =  HG / AB

 

GF / 48   =   12 / 72

 

GF   =   48 * 12 / 72

 

GF   =   8

 

 

2)

Since  \(\frac{21}{42}\,=\,\frac{9}{18}\)    , the sides are proportional.

 

And the included angle is the same.

 

So by   SAS  ,   △FGH ~ △UVW

 

 

3)

By the AA theorem, △ABC ~ △EDC . So

 

AB / AC  =  ED / EC

 

15 / 18   =   31.5 / x

 

x * 15 / 18  =  31.5

 

x   =   31.5 * 18 / 15

 

x   =   37.8