Question

1.) if pq = qr, with pq = 3x - 8, qr = 2x, and rs = 1.5x + 4, then ps = 24.

Explanation:

Step1: Set up the equation from the given condition

Since \(PQ = QR\) and \(PQ=3x - 8\), \(QR = 2x\), we have \(3x-8=2x\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(3x-2x - 8=2x-2x\), which gives \(x - 8=0\). Then add 8 to both sides, so \(x=8\).

Step3: Find the lengths of \(QR\) and \(RS\)

Substitute \(x = 8\) into the expressions for \(QR\) and \(RS\). \(QR=2x=2\times8 = 16\), \(RS=1.5x + 4=1.5\times8+4=12 + 4=16\).

Step4: Calculate \(PS\)

Since \(PS=PQ + QR+RS\), and \(PQ = QR=RS = 16\) (from previous steps), \(PS=16+16 + 16=48\)

Answer:

48