Question

if $qr = 5$, $rs=x + 10$, and $qs = 4x$, 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: $4x=5+(x + 10)$.

Step2: Simplify the right - hand side

$4x=5+x + 10$, which simplifies to $4x=x + 15$.

Step3: Solve for x

Subtract x from both sides: $4x−x=x + 15−x$, so $3x=15$. Then divide both sides by 3: $x = 5$.

Step4: Find the value of RS

Substitute $x = 5$ into the expression for $RS$. Since $RS=x + 10$, then $RS=5 + 10=15$.

Answer:

15