Question

point s is on line segment rt. given st = 3x - 8, rt = 4x, and rs = 4x - 7, determine the numerical length of rt.

Explanation:

Step1: Use the segment addition postulate

Since \(S\) is on \(\overline{RT}\), \(RS + ST=RT\).
Substitute the given expressions: \((4x - 7)+(3x - 8)=4x\).

Step2: Simplify the left - hand side of the equation

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

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 \(RT\)

Since \(RT = 4x\), substitute \(x = 5\) into the expression. Then \(RT=4\times5\).

Answer:

\(20\)