Answer:
12 units
Step-by-step explanation:
All of the right triangles in this figure are similar, so corresponding sides have the same ratio.
short side / long side = 9/x = x/16
x^2 = 144 . . . . . cross multiply
x = √144 = 12
The value of x is 12 units.
_____
Comment on this geometry
The value of x is the "geometric mean" of 9 and 16. That is ...
RT = √(ST·QT)
There are other geometric mean relationships in this figure as well, all of which derive from the fact the triangles are similar.
RS = √(TS·QS)
RQ = √(TQ·SQ)
