Use Pythagoras theorem to find the lengths of blue lines.
Total length
= 4/2 + 6/2 + 8/2 + \(\sqrt{(\dfrac{4}{2})^2+(\dfrac{6}{2})^2}+\sqrt{(\dfrac{8}{2})^2+(\dfrac{4}{2})^2}+\sqrt{(\dfrac{6}{2})^2+(\dfrac{8}{2})^2}\)
= 2 + 3 + 4 + \(\sqrt{13}\) + \(2\sqrt{5}\) + 5
= 14 + sqrt(13) + 2sqrt(5)