Question: Find $UV$ in rectangle $TUVW$.
$U$
$2x-81$
$V$
$3x-98$
$x$
$T$
$W$
$UV = $
1. **State the problem:** We need to find the length of side $UV$ in rectangle $TUVW$.
2. **Recall properties of rectangles:** Opposite sides of a rectangle are equal in length. So, $UV = TW$ and $TU = VW$.
3. **Given:**
- $UV = 2x - 81$
- $TU = 3x - 98$
- $VW = x$
Since $TU$ and $VW$ are opposite sides, they must be equal:
$$3x - 98 = x$$
4. **Solve for $x$:**
$$3x - 98 = x$$
$$3x - \cancel{x} - 98 = \cancel{x}$$
$$2x - 98 = 0$$
$$2x = 98$$
$$x = \frac{98}{2}$$
$$x = 49$$
5. **Find $UV$ by substituting $x=49$ into $2x - 81$:**
$$UV = 2(49) - 81$$
$$UV = 98 - 81$$
$$UV = 17$$
**Final answer:**
$$\boxed{17}$$