Question

if l - m - n, and if lm = 2x, mn = 3x - 1, and ln = 24, then find mn. after you enter your answer press go. mn =

Explanation:

Step1: Use segment addition postulate

Since \(L - M - N\), we have \(LM+MN = LN\). Substituting the given values: \(2x+(3x - 1)=24\).

Step2: Simplify the equation

Combine like - terms: \(2x+3x-1 = 24\), which gives \(5x-1 = 24\).

Step3: Solve for \(x\)

Add \(1\) to both sides: \(5x=24 + 1=25\). Then divide both sides by \(5\): \(x=\frac{25}{5}=5\).

Step4: Find \(MN\)

Substitute \(x = 5\) into the expression for \(MN\). Since \(MN=3x - 1\), then \(MN=3\times5-1\).
Calculate \(3\times5-1=15 - 1=14\).

Answer:

\(14\)