You can bind B’s Width and Height to that of A’s. For example, in the XAML where you define B:
[XAML]
<local:B Width='{Binding RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type A}}, Path=Width}' /local:B>
If there is an ActualWidth property in A, then you might want to bind B’s Width to that instead. Do the same for Height.
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