Question

In right triangle RST below, altitude SV is drawn to hypotenuse RT. If RV =4.1 and TV =10.2,what is the length of ST to the nearest length? 1. 7.7 2. 6.5 3. 12.1 4. 11.0

Answer 1

12.1 (option 3)

Step-by-step explanation:

We would apply geometric mean formula:

`(leg)/(TV)=\frac{RT}{\text{leg}}`

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

`\begin{gathered} (ST)/(10.2)=(14.3)/(ST) \\ \text{cross multiply:} \\ ST(ST)\text{ = 10.2(14.3)} \\ ST^2\text{ = }145.86 \end{gathered}`
`\begin{gathered} \text{square root both sides:} \\ \sqrt[]{ST^2}\text{ = }\sqrt[]{145.86} \\ ST\text{ = 12.077} \end{gathered}`

To the nearest tenth, ST is 12.1 (option 3)