Question

point s is on line segment $overline{rt}$. given $rt = 3x$, $rs = 3x - 5$, and $st = 3x - 1$, determine the numerical length of $overline{rt}$.

Explanation:

Step1: Use segment - addition postulate

Since point S is on line segment $\overline{RT}$, we know that $RT=RS + ST$. Substitute the given expressions: $3x=(3x - 5)+(3x - 1)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $3x=3x-5 + 3x-1=6x-6$.

Step3: Solve for x

Subtract $3x$ from both sides: $0 = 6x-3x-6$, which simplifies to $0 = 3x-6$. Then add 6 to both sides: $3x=6$, and divide by 3 to get $x = 2$.

Step4: Find the length of $\overline{RT}$

Substitute $x = 2$ into the expression for $RT$. Since $RT = 3x$, then $RT=3\times2=6$.

Answer:

6