Question

point s is on line segment \overline{rt}. given rt = x + 5, st = 4x - 9, and rs = x - 2, determine the numerical length of \overline{rt}. answer attempt 1 out of 2 rt =

Explanation:

Step1: Use the segment addition postulate

Since \(S\) is on \(\overline{RT}\), we have \(RT = RS+ST\).
Substitute the given expressions: \(x + 5=(x - 2)+(4x-9)\).

Step2: Simplify the right - hand side of the equation

\((x - 2)+(4x-9)=x-2 + 4x-9=5x-11\). So the equation becomes \(x + 5=5x-11\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(5 = 4x-11\).
Add \(11\) to both sides: \(16 = 4x\).
Divide both sides by \(4\): \(x = 4\).

Step4: Find the length of \(RT\)

Substitute \(x = 4\) into the expression for \(RT\): \(RT=x + 5\).
So \(RT=4 + 5\).

Answer:

\(9\)