Question

point s lies between points r and t on \\(\overline{rt}\\). if rt is 10 centimeters long, what is st? \\(\bigcirc\\) 2 centimeters \\(\bigcirc\\) 4 centimeters \\(\bigcirc\\) 6 centimeters \\(\bigcirc\\) 8 centimeters

Explanation:

Step1: Find the length of RT in terms of x

Since S is between R and T, \( RT = RS + ST \). Given \( RS = 2x \) and \( ST = 3x \), then \( RT = 2x + 3x = 5x \).

Step2: Solve for x using RT = 10

We know \( RT = 10 \) cm and \( RT = 5x \), so \( 5x = 10 \). Dividing both sides by 5, we get \( x = \frac{10}{5} = 2 \).

Step3: Find the length of ST

Since \( ST = 3x \) and \( x = 2 \), then \( ST = 3\times2 = 6 \) cm.

Answer:

6 centimeters