Use the geometric mean involving altitudes. That will be [tex] \frac{ST}{RT}= \frac{RT}{QT} [/tex]. Filling in our values for the legs of that triangle our proportion then looks like this: [tex] \frac{9}{x}= \frac{x}{16} [/tex]. Cross multiply to get [tex] x^{2} =144[/tex]. Taking the principle value of that square root, we get that x = 12.
