How to keep the size ratio of a object as it is re sized?

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XAML

Silverlight

Hi,

I have objects (lets say buttons) placed in a column in a grid.
The width of the column can be changed by the user with help of a grid splitter.
The buttons should have the same width as the column and each of them should have the same height as width.

My problem is to figure out a way to make the objects change their height as the width of the column changes.

The XAML below just describes what I want to accomplish.
It does not work. The height should of course be updated when the actual width changes.

<Grid.ColumnDefinitions>
                <ColumnDefinition Width="100"/>
                <ColumnDefinition Width="2"/>
                <ColumnDefinition Width="*"/>
            </Grid.ColumnDefinitions>
            <controls:GridSplitter Grid.Row="1" Grid.Column="1" Grid.RowSpan="3" HorizontalAlignment="Stretch" VerticalAlignment="Stretch" ShowsPreview="True" />
            <Grid Name="widgetPanel"  Grid.Row="1" Grid.Column="0" VerticalAlignment="Center">
                <StackPanel>
                    <Button Height="{Binding ActualWidth, ElementName=_widgetPanel}" />
                    <Button Height="{Binding ActualWidth, ElementName=_widgetPanel}" />
                    <Button Height="{Binding ActualWidth, ElementName=_widgetPanel}" />
                    <Button Height="{Binding ActualWidth, ElementName=_widgetPanel}" />
                </StackPanel>
            </Grid>
</Grid>

Any suggestions are welcome!