consider the diagram. what is qs? o 2 units. o 5 units. o 17 units. o 33 units. r t q 3x + 2 5x - 8 s

Explanation:

Step1: Set up equation

Since $\triangle RTS\cong\triangle QTS$ (by the property of perpendicular bisector, $l$ is the perpendicular bisector of $RQ$), then $RS = QS$. So we set $3x + 2=5x - 8$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $2 = 5x-3x - 8$, which simplifies to $2=2x - 8$. Then add 8 to both sides: $2 + 8=2x$, so $10 = 2x$. Divide both sides by 2, we get $x = 5$.

Step3: Find $QS$

Substitute $x = 5$ into the expression for $QS$ which is $5x-8$. So $QS=5\times5 - 8=25 - 8=17$.

Answer:

17 units