Question

t is a point on segment \\( \overline { s u } \\). if \\( s t = x + 6 \\), \\( t u = 5 x \\), and \\( s u = 18 \\), what is tu? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

Since \(T\) is on segment \(\overline{SU}\), by the segment addition postulate \(ST + TU=SU\).
Substitute \(ST = x + 6\), \(TU = 5x\), and \(SU = 18\) into the equation: \((x + 6)+5x=18\).

Step2: Simplify the left - hand side

Combine like terms: \(x+5x + 6=18\), which gives \(6x+6 = 18\).

Step3: Solve for \(x\)

Subtract \(6\) from both sides: \(6x+6-6=18 - 6\), so \(6x=12\).
Divide both sides by \(6\): \(x=\frac{12}{6}=2\).

Step4: Find the length of \(TU\)

Substitute \(x = 2\) into the expression for \(TU\). Since \(TU = 5x\), then \(TU=5\times2 = 10\).

Answer:

\(10\)