There isn't a direct API for detecting the screen width and height from within a Silverlight app. Fortunately, JavaScript provides you a way, viz. via the screen.width and screen.height properties. So with a nifty use of Silverlight's HTML DOM Bridge, these values can be read with little issue.
int screenWidth = Int32.Parse(
HtmlPage.Window.Eval("screen.width").ToString()
);
int screenHeight = Int32.Parse(
HtmlPage.Window.Eval("screen.height").ToString()
);
Then when your app runs in fullscreen mode, you'd get the screen resolution using the Silverlight plug-in's ActualWidth and ActualHeight.
int screenWidth =
Application.Current.Host.Content.ActualWidth;
int screenHeight =
Application.Current.Host.Content.ActualHeight;
Read: How to tell the screen resolution from within a Silverlight app