Question

point s is on line segment \overline{rt}. given st = 3x - 8, rt = 4x, and rs = 4x - 7, 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 \(RS + ST=RT\).
Substitute the given expressions: \((4x - 7)+(3x - 8)=4x\).

Step2: Simplify the left - hand side

Combine like terms: \(4x+3x - 7 - 8=4x\), which gives \(7x-15 = 4x\).

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(7x-4x-15=4x - 4x\), so \(3x-15 = 0\).
Add \(15\) to both sides: \(3x=15\).
Divide both sides by \(3\): \(x = 5\).

Step4: Find the length of \(RT\)

Substitute \(x = 5\) into \(RT = 4x\). So \(RT=4\times5\).

Answer:

\(20\)