Answer
$y = 3$
Both $ST$ and $TU$ are 15.
Work Step by Step
The angle bisector theorem states that a point that is located on an angle's bisector is equidistant from the angle's sides.
In this diagram, we see that $\overline{TV}$ is the angle bisector of $\angle SVU$. Therefore, $T$, which is a point on the bisector, is equidistant from the sides of the angle. So, $T$ is equidistant from $\overline{VS}$ and $\overline{VU}$. Therefore, $\overline{ST}$ is equal to $\overline{TU}$.
Let's set $ST$ and $TU$ equal to one another to find the value of $y$:
$5y = 3y + 6$
Subtract $3y$ from each side to isolate the variable on one side of the equation:
$2y = 6$
Divide each side of the equation by $2$ to solve for $y$:
$y = 3$
$ST = TU = 5y$
Plug in $3$ for $y$:
$ST = TU = 5(3)$
Multiply to solve:
$ST = TU = 15$
