Question

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

Explanation:

Step1: Set up equation based on line - segment addition

Since point S lies between R and T, $RT=RS + ST$. Given $RS = 2x$, $ST=3x$, and $RT = 10$ cm, we have the equation $2x+3x=10$.
$2x + 3x=10$

Step2: Combine like - terms

Combining the left - hand side of the equation, we get $5x = 10$.
$5x=10$

Step3: Solve for x

Divide both sides of the equation by 5.
$x=\frac{10}{5}=2$

Step4: Find the length of ST

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

Answer:

C. 6 centimeters