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 have $3x - 8=2x$.
Solve for $x$:
$3x-2x = 8$, so $x = 8$.

Step2: Find lengths of segments

We know $QR = 2x$. Substitute $x = 8$, then $QR=2\times8 = 16$.
$PQ=QR = 16$.
$RS=1.5x + 4$, substitute $x = 8$, then $RS=1.5\times8+4=12 + 4=16$.

Step3: Calculate length of PS

$PS=PQ + QR+RS$.
$PS=16+16 + 16=48$.

Answer:

D. 48