Respuesta :

gmany
The traingle RQT and the triangle SRT are similar. Therefore:
[tex]\dfrac{x}{9}=\dfrac{16}{x}\ \ \ \ |\text{cross multiply}\\\\x\cdot x=9\cdot16\\\\x^2=9\cdot16\to x=\sqrt{9\cdot16}\\\\x=\sqrt9\cdot\sqrt{16}\\\\x=3\cdot4\\\\\boxed{x=12\ \text{units}}[/tex]
Triangles STR and  RTQ are similar so corresponding sides are in the same ratio.

So we have :-
x/16 = 9/x
x^2 = 144 
x = 12 (answer)