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)

Explanation:

We would apply geometric mean formula:

$\frac{leg}{TV}=\frac{RT}{\text{leg}}$

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} \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}$$\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)