how to bind width of child element to width of parent element in silverlight

 Width="{Binding Width, RelativeSource={RelativeSource AncestorType={x:Type Parent}, Mode=FindAncestor}}"

if both controls DataContext is different.

I think that easiest way to do same thing is:

HorizontalAlignment="Stretch"

That is not using binding as you have been asked, but it is easier.

This will actually help you I guess

Width="{Binding ActualWidth, ElementName=parentElementName}"

This binds the width to the parent element or the element name provided

This is generic solution which may work everywhere. You wouldn't need to write parent element name. This will identify its parent and will take parent's width.

Width="{Binding RelativeSource={RelativeSource TemplatedParent}, Path=ActualWidth}"