Question

true or false: if $overline{pq}congoverline{qr}$, with $pq = 3x - 8$, $qr = 2x$, and $rs = 1.5x + 4$, then $ps = 24$.
p q r s
true
false

Explanation:

Step1: Set up equation from congruence

Since $\overline{PQ}\cong\overline{QR}$, we have $PQ = QR$. 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, $x=8$.

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 PS

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

Answer:

False