Question

t is the midpoint of \\(\overline{su}\\). if \\(tu = x + 8\\) and \\(su = 4x + 8\\), what is \\(tu\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( T \) is the midpoint of \( \overline{SU} \), \( SU = 2 \times TU \).
Given \( TU = x + 8 \) and \( SU = 4x + 8 \), so \( 4x + 8 = 2(x + 8) \).

Step2: Solve for \( x \)

Expand the right side: \( 4x + 8 = 2x + 16 \).
Subtract \( 2x \) from both sides: \( 4x - 2x + 8 = 16 \), which simplifies to \( 2x + 8 = 16 \).
Subtract 8 from both sides: \( 2x = 16 - 8 = 8 \).
Divide both sides by 2: \( x = \frac{8}{2} = 4 \).

Step3: Find \( TU \)

Substitute \( x = 4 \) into \( TU = x + 8 \): \( TU = 4 + 8 = 12 \).

Answer:

\( 12 \)