Look at the picture.
[tex]\Delta ADC\ and\ \Delta CDB\ are\ similar\ therefore\\\\\dfrac{y}{4}=\dfrac{9}{y}\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot9\\\\y^2=36\to y=\sqrt{36}\to y=6[/tex]
Use Pythagorean theorem.
[tex]z^2=6^2+9^2\\\\z^2=36+81\\\\z^2=117\\\\z=\sqrt{117}\\\\z=\sqrt{9\cdot13}\\\\z=\sqrt9\cdot\sqrt{13}\\\\\boxed{z=3\sqrt{13}}[/tex]
