Question

l is the mid - point of km. if kl = 10x and lm = 5x + 10, what is kl? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(L\) is the mid - point of \(XM\), then \(XL = LM\). So, \(10x=5x + 10\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides of the equation \(10x=5x + 10\). We get \(10x-5x=5x + 10-5x\), which simplifies to \(5x=10\). Then divide both sides by \(5\): \(\frac{5x}{5}=\frac{10}{5}\), so \(x = 2\).

Step3: Find \(XL\)

Substitute \(x = 2\) into the expression for \(XL\). Since \(XL=10x\), then \(XL=10\times2=20\).

Step4: Find \(XM\)

Since \(XM=XL + LM\) and \(XL = LM = 20\), then \(XM=20+20 = 40\).

Answer:

40