Question

What is the value of x?

Answer 1

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