Answer:
x = 12 units
Step-by-step explanation:
ΔQTR and ΔRTS are similar (AAA). Therefore the corresponding sides are in proportion:
[tex]\dfrac{RT}{TS}=\dfrac{TQ}{RT}[/tex]
We have
[tex]RT=x,\ TS=9,\ TQ=16[/tex]
Substitute:
[tex]\dfrac{x}{9}=\dfrac{16}{x}[/tex] cross multiply
[tex]x^2=(9)(16)\\\\x^2=144\to x=\sqrt{144}\\\\x=12[/tex]
