Question

if t is the midpoint of \\(\overline{su}\\), find the values of x and st. the diagram is not to scale.
s t u
9x 4x+25
x=\square
st=\square

Explanation:

Step1: Use midpoint definition

Since T is the midpoint of \( \overline{SU} \), \( ST = TU \). So \( 9x = 4x + 25 \).

Step2: Solve for x

Subtract \( 4x \) from both sides: \( 9x - 4x = 25 \), which simplifies to \( 5x = 25 \). Then divide both sides by 5: \( x = \frac{25}{5} = 5 \).

Step3: Find ST

Substitute \( x = 5 \) into \( ST = 9x \): \( ST = 9 \times 5 = 45 \).

Answer:

\( x = 5 \), \( ST = 45 \)