Question

point s is on line segment $overline{rt}$. given $rt = 2x$, $rs = 3x - 8$, and $st = x$, determine the numerical length of $overline{st}$. answer attempt 1 out of 2 $st=$

Explanation:

Step1: Use segment - addition postulate

Since point S is on line segment $\overline{RT}$, we know that $RT=RS + ST$. Substituting the given expressions: $2x=(3x - 8)+x$.

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $(3x - 8)+x=3x+x - 8=4x - 8$. So the equation becomes $2x=4x - 8$.

Step3: Solve for x

Subtract $2x$ from both sides: $0 = 4x-2x - 8$, which simplifies to $0 = 2x - 8$. Then add 8 to both sides: $2x=8$. Divide both sides by 2: $x = 4$.

Step4: Find the length of ST

Since $ST=x$, and we found that $x = 4$, then $ST = 4$.

Answer:

$4$