Question

if qr = 13x, rs = 2x + 16, and qs = 13x + 20, what is qr? diagram of q---r---s with qr labeled 13x, rs labeled 2x + 16, qs labeled 13x + 20 simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

We know that \( QS = QR + RS \). Substituting the given expressions: \( 13x + 20 = 13x + (2x + 16) \)

Step2: Solve for \( x \)

Simplify the equation: \( 13x + 20 = 15x + 16 \). Subtract \( 13x \) from both sides: \( 20 = 2x + 16 \). Subtract 16: \( 4 = 2x \). Divide by 2: \( x = 2 \)

Step3: Find \( QR \)

Given \( QR = 13x \), substitute \( x = 2 \): \( QR = 13\times2 = 26 \)

Answer:

26