Question

if $qr = 6x, rs = 13x + 5$, and $qs = 17x + 17$, what is $rs?
simplify your answer and write it as a proper fraction, mixed number, or integer

Explanation:

Step1: Use segment - addition postulate

Since $QS=QR + RS$, we substitute the given expressions: $17x + 17=6x+(13x + 5)$.

Step2: Simplify the right - hand side

$6x+(13x + 5)=6x+13x + 5=19x + 5$. So the equation becomes $17x + 17=19x + 5$.

Step3: Solve for x

Subtract $17x$ from both sides: $17x+17-17x=19x + 5-17x$, which gives $17 = 2x+5$. Then subtract 5 from both sides: $17 - 5=2x+5 - 5$, so $12 = 2x$. Divide both sides by 2: $\frac{12}{2}=\frac{2x}{2}$, and $x = 6$.

Step4: Find the value of RS

Substitute $x = 6$ into the expression for $RS$. Since $RS=13x + 5$, then $RS=13\times6+5$. Calculate $13\times6+5=78 + 5=83$.

Answer:

83