Question

if kl = 11x, lm = x + 14, and km = 16x + 2, what is lm?
k l m
11x x + 14
16x + 2
simplify your answer and write it as a proper fraction, mixed number, or integer.
submit

Explanation:

Step1: Use segment addition postulate

From the diagram, \( KM = KL + LM \). Substitute the given expressions: \( 16x + 2 = 11x + (x + 14) \).

Step2: Simplify and solve for \( x \)

Simplify the right - hand side: \( 16x+2 = 12x + 14 \). Subtract \( 12x \) from both sides: \( 16x-12x + 2=12x - 12x+14 \), which gives \( 4x + 2=14 \). Subtract 2 from both sides: \( 4x+2 - 2=14 - 2 \), so \( 4x = 12 \). Divide both sides by 4: \( x=\frac{12}{4}=3 \).

Step3: Find the length of \( LM \)

Since \( LM=x + 14 \) and \( x = 3 \), substitute \( x \) into the expression for \( LM \): \( LM=3 + 14=17 \).

Answer:

\( 17 \)