Question

if $pqcong qr$ with $pq = 3x - 8$, $qr = 2x$, and $rs=1.5x + 4$ then find the length of $ps$.

Explanation:

Step1: Set up equation from congruence

Since $PQ\cong QR$, we set $PQ = QR$. So, $3x - 8=2x$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $3x-2x - 8=2x-2x$, which gives $x - 8=0$. Then add 8 to both sides, we get $x = 8$.

Step3: Find lengths of segments

$PQ=3x - 8=3\times8 - 8=24 - 8 = 16$, $QR = 2x=2\times8 = 16$, $RS=1.5x + 4=1.5\times8+4=12 + 4=16$.

Step4: Calculate length of $PS$

$PS=PQ + QR+RS$. Substitute the values: $PS=16 + 16+16=48$.

Answer:

B. 48