Question

r is a point on segment \\(\overline{qs}\\). if \\(qr = 13x\\), \\(rs = x + 5\\), and \\(qs = 19\\), what is \\(qr\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( R \) is on \( \overline{QS} \), we have \( QR + RS = QS \). Substituting the given expressions, we get \( 13x+(x + 5)=19 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 14x+5 = 19 \). Subtract 5 from both sides: \( 14x=19 - 5=14 \). Then divide both sides by 14: \( x = \frac{14}{14}=1 \).

Step3: Find \( QR \)

Since \( QR = 13x \) and \( x = 1 \), substitute \( x \) into the expression for \( QR \): \( QR=13\times1 = 13 \).

Answer:

13