solve for $x$. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Apply Triangle Proportionality Theorem

Since $UT \parallel RQ$, the segments created on the sides of the triangle are proportional: $\frac{SU}{SR} = \frac{ST}{SQ}$ which rearranges to $\frac{SU}{UR} = \frac{ST}{TQ}$

Step2: Substitute known values

$\frac{10}{x} = \frac{12}{6}$

Step3: Cross-multiply to solve for $x$

$12x = 10 \times 6$ $12x = 60$ $x = \frac{60}{12}$

Answer:

$5$