Questions: L is the midpoint of KM. If KL=5x and LM=x+4, what is KL?

Transcript text: $L$ is the midpoint of $\overline{K M}$. If $K L=5 x$ and $L M=x+4$, what is $K L$ ?

Solution

Step 1: Understand the Problem

We are given that $ L $ is the midpoint of $ KM $. We need to find the length of $ KL $ given that $ KL = 5x $ and $ LM = x + 4 $.

Step 2: Use the Midpoint Property

Since $ L $ is the midpoint of $ KM $, the lengths $ KL $ and $ LM $ are equal. Therefore, we can set up the equation: \[ KL = LM \]

Step 3: Set Up the Equation

Given $ KL = 5x $ and $ LM = x + 4 $, we set up the equation: \[ 5x = x + 4 \]

Step 4: Solve for $ x $

Subtract $ x $ from both sides of the equation: \[ 5x - x = 4 \] \[ 4x = 4 \] Divide both sides by 4: \[ x = 1 \]

Step 5: Find $ KL $

Substitute $ x = 1 $ back into the expression for $ KL $: \[ KL = 5x = 5(1) = 5 \]

\[ KL = 5 \]

Was this solution helpful?

Unhelpful

Helpful

Thank you for your feedback.

Copied!