Question

what is the length of ps, when r is the midpoint of ps? 7x - 5 4(x + 1) p r s 3 16 23 32

Explanation:

Step1: Set up equation using mid - point property

Since \(R\) is the mid - point of \(PS\), 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 \(PS\)

\(PS=PR + RS\). Since \(PR = 7x−5\) and \(RS = 4(x + 1)\), and \(x = 3\), then \(PR=7\times3−5=21 - 5=16\) and \(RS=4\times(3 + 1)=4\times4 = 16\). So \(PS=16+16=32\).

Answer:

32