Question

if kl = x + 8, lm = 20, and km = 5x + 16, what is kl? diagram of k---l---m with kl labeled x+8, lm labeled 20, km labeled 5x+16 simplify your answer and write it as a proper fraction, mixed number, or integer

Explanation:

Step1: Use segment addition postulate

From the diagram, \( KM = KL + LM \). Substitute the given expressions: \( 5x + 16=(x + 8)+20 \)

Step2: Solve for \( x \)

Simplify the right side: \( 5x + 16=x + 28 \)
Subtract \( x \) from both sides: \( 4x + 16 = 28 \)
Subtract 16 from both sides: \( 4x=12 \)
Divide by 4: \( x = 3 \)

Step3: Find \( KL \)

Substitute \( x = 3 \) into \( KL=x + 8 \): \( KL=3 + 8=11 \)

Answer:

11