Question

what is the length of $overline{ps}$, when $r$ is the mid - point of $overline{ps}$?
$7x - 5$ $4(x + 1)$
a 23
b 32
c 16
d 3

Explanation:

Step1: Set up the equation

Since \(R\) is the mid - point of \(\overline{PS}\), then \(PR = RS\). So, \(7x−5 = 4(x + 1)\).

Step2: Expand and solve for \(x\)

Expand \(4(x + 1)\) to get \(4x+4\). Then the equation becomes \(7x−5 = 4x + 4\). Subtract \(4x\) from both sides: \(7x-4x−5=4x - 4x+4\), which simplifies to \(3x−5 = 4\). Add 5 to both sides: \(3x-5 + 5=4 + 5\), so \(3x=9\). Divide both sides by 3: \(x = 3\).

Step3: Find the length of \(PR\) or \(RS\)

Substitute \(x = 3\) into the expression for \(PR\): \(PR=7x−5=7\times3−5=21 - 5=16\).

Step4: Find the length of \(PS\)

Since \(PS=PR + RS\) and \(PR = RS\), then \(PS = 2PR\). So \(PS=2\times16 = 32\).

Answer:

B. 32