Question

use the segment addition postulate to find the length of $overline{st}$ if $overline{sr}=2x + 7$, $overline{st}=x - 6$ and $overline{rt}=100$. $overline{st}=\text{______ units}$

Explanation:

Step1: Apply segment - addition postulate

By the Segment Addition Postulate, $\overline{SR}+\overline{ST}=\overline{RT}$. Substitute the given expressions: $(2x + 7)+(x - 6)=100$.

Step2: Simplify the left - hand side

Combine like terms: $2x+x+7 - 6=100$, which simplifies to $3x + 1=100$.

Step3: Solve for $x$

Subtract 1 from both sides: $3x=100 - 1=99$. Then divide both sides by 3: $x=\frac{99}{3}=33$.

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

Substitute $x = 33$ into the expression for $\overline{ST}$. $\overline{ST}=x - 6$. So $\overline{ST}=33 - 6=27$.

Answer:

27