Question

if kl = 11x, lm = 6x - 13, and km = 16x + 1, what is km?
diagram: line segment k---l---m with kl labeled 11x, lm labeled 6x - 13, km labeled 16x + 1
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( KL + LM = KM \). Substitute the given expressions: \( 11x + (6x - 13) = 16x + 1 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 17x - 13 = 16x + 1 \). Subtract \( 16x \) from both sides: \( x - 13 = 1 \). Add 13 to both sides: \( x = 14 \).

Step3: Find \( KM \)

Substitute \( x = 14 \) into \( KM = 16x + 1 \): \( KM = 16(14) + 1 \). Calculate: \( KM = 224 + 1 = 225 \).

Answer:

225