Question

point s is on line segment $overline{rt}$. given $rt = 5x - 4$, $st = 3x$, and $rs = x$, determine the numerical length of $overline{rs}$.

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: $5x-4=x + 3x$.

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $x + 3x=4x$. So the equation becomes $5x-4 = 4x$.

Step3: Solve for x

Subtract $4x$ from both sides of the equation: $5x-4x-4=4x-4x$.
This simplifies to $x - 4=0$. Then add 4 to both sides: $x=4$.

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

We know that $RS=x$. Since $x = 4$, then $RS = 4$.

Answer:

4