12.1 (option 3)
Explanation:
We would apply geometric mean formula:
[tex]\frac{leg}{TV}=\frac{RT}{\text{leg}}[/tex]
RV = 4.1
TV =10.2
We have 2 legs: ST and SR but since we are looking for ST:
ST = leg
RT = RV + TV = 4.1 + 10.2 = 14.3
[tex]\begin{gathered} \frac{ST}{10.2}=\frac{14.3}{ST} \\ \text{cross multiply:} \\ ST(ST)\text{ = 10.2(14.3)} \\ ST^2\text{ = }145.86 \end{gathered}[/tex][tex]\begin{gathered} \text{square root both sides:} \\ \sqrt[]{ST^2}\text{ = }\sqrt[]{145.86} \\ ST\text{ = 12.077} \end{gathered}[/tex]
To the nearest tenth, ST is 12.1 (option 3)
