Question

l is the midpoint of (overline{km}). if (kl = 4x) and (km = 6x + 6), what is (km)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the mid - point property

Since \(L\) is the mid - point of \(\overline{KM}\), then \(KM = 2KL\).
Given \(KL = 4x\) and \(KM=6x + 6\), we substitute into the equation \(KM = 2KL\). So, \(6x+6=2\times(4x)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(6x + 6=8x\).
Subtract \(6x\) from both sides: \(6=8x-6x\).
Simplify: \(6 = 2x\).
Divide both sides by \(2\): \(x = 3\).

Step3: Find the value of \(KM\)

Substitute \(x = 3\) into the expression for \(KM\).
\(KM=6x+6\), so \(KM=6\times3 + 6\).
First, calculate \(6\times3=18\), then \(18 + 6=24\).

Answer:

\(24\)