Question

apply the segment addition postulate to find the length of given: point s lies between - r and t on $overline{rt}$ $rs = 2x - 4$ $st = 8$ $rt=x + 11$ find: rs and rt

Explanation:

Step1: Apply segment - addition postulate

Since point $S$ lies between $R$ and $T$, we have $RS + ST=RT$. Substitute the given expressions: $(2x - 4)+8=x + 11$.

Step2: Simplify the left - hand side

Combine like terms on the left - hand side of the equation: $2x+(8 - 4)=2x + 4$. So, $2x+4=x + 11$.

Step3: Solve for $x$

Subtract $x$ from both sides: $2x - x+4=x - x + 11$, which gives $x+4 = 11$. Then subtract 4 from both sides: $x=11 - 4=7$.

Step4: Find the length of $RS$

Substitute $x = 7$ into the expression for $RS$: $RS=2x - 4=2\times7 - 4=14 - 4 = 10$.

Step5: Find the length of $RT$

Substitute $x = 7$ into the expression for $RT$: $RT=x + 11=7+11 = 18$.

Answer:

$RS = 10$, $RT = 18$