Question

What is the value of x?

Answer 1

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