We are given a trapezoid $HJKT$. $TS$ is the midsegment of the trapezoid. We are given that $HJ = 14$ and $LK = 42$. We need to find the length of $TS$.

1. Problem Description

We are given a trapezoid $HJKT$. $TS$ is the midsegment of the trapezoid. We are given that $HJ = 14$ and $LK = 42$. We need to find the length of $TS$.

2. Solution Steps

The midsegment of a trapezoid is the segment that connects the midpoints of the two non-parallel sides. The midsegment is parallel to the bases, and its length is the average of the lengths of the bases.

In this case, the bases are $HJ$ and $LK$, and $TS$ is the midsegment. Therefore,

$TS = \frac{HJ + LK}{2}$.

We are given that $HJ = 14$ and $LK = 42$.

Substituting these values into the formula, we get:

$TS = \frac{14 + 42}{2}$

$TS = \frac{56}{2}$

$TS = 28$

3. Final Answer

28