In this problem, we are dealing with a rectangle, STUV. In a rectangle, opposite sides are equal in length. Therefore, the length of side $SW$ will be equal to the length of side $UV$.

Since you have provided expressions for $UW = 4t + 37$ and $VW = 7t + 34$, I assume that the length $SW$ corresponds to either $UW$ or $VW$, and we are likely working with a scenario where you need to solve for $t$ and then calculate the length of $SW$.

Let's clarify:

• The rectangle’s sides $ST$ and $UV$ are equal, and $SU$ and $TV$ are equal.
• $UW$ and $VW$ might be diagonals or segments related to one of the sides.

Please confirm if these segments are indeed sides of the rectangle or if you have additional context to help refine the solution.