I think the easiest way is to scale the graphics output to the destination rectangle:
public static class GraphicsExtensions
{
public static void DrawStringInside(this Graphics graphics, Rectangle rect, Font font, Brush brush, string text)
{
var textSize = graphics.MeasureString(text, font);
var state = graphics.Save();
graphics.TranslateTransform(rect.Left, rect.Top);
graphics.ScaleTransform(rect.Width / textSize.Width, rect.Height / textSize.Height);
graphics.DrawString(text, font, brush, PointF.Empty);
graphics.Restore(state);
}
}
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