This below code shows how to animate the width and height of a border element in WPF and XAML.
<Page x:Class="BorderSamples.Page1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Page1">
<StackPanel Orientation="Vertical" HorizontalAlignment="Center">
<Border Background="#99FFFFFF" BorderBrush="#CCCCFF" BorderThickness="1"
Margin="0,60,0,20" Padding="20" >
<Border.Triggers>
<EventTrigger RoutedEvent="Border.Loaded">
<BeginStoryboard>
<Storyboard>
<ThicknessAnimation
Storyboard.TargetProperty="BorderThickness"
Duration="0:0:1.5" FillBehavior="HoldEnd" From="1,1,1,1" To="14,14,14,14" />
</Storyboard>
</BeginStoryboard>
</EventTrigger>
</Border.Triggers>
<TextBlock>
Border animation
</TextBlock>
</Border>
</StackPanel>
</Page>