Question

1. $overline{qs}$ is 60 units in length. find $qr$.

Explanation:

Step1: Set up the equation

Since \(QS = QR + RS\), we have \((5x + 4)+(16 + 3x)=60\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \(5x+3x+4 + 16=60\), which simplifies to \(8x+20 = 60\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(8x+20-20=60 - 20\), so \(8x=40\). Then divide both sides by 8: \(x=\frac{40}{8}=5\).

Step4: Find \(QR\)

Substitute \(x = 5\) into the expression for \(QR\) (\(QR=5x + 4\)). So \(QR=5\times5+4=25 + 4=29\).

Answer:

\(29\)