1. **State the problem:** We have a trapezoid with bases of lengths 5 (longer base) and 2 (shorter base), and height 1. There is a dotted line inside the trapezoid parallel to the bases, and we need to find its length rounded to the nearest tenth. 2. **Recall the formula for a line segment parallel to the bases inside a trapezoid:** The length of a segment parallel to the bases at a certain height $h$ from the shorter base can be found by linear interpolation between the two bases. If the trapezoid height is $H$, and the segment is at height $h$ from the shorter base, then the length $L$ of the segment is: $$L = b_1 + \frac{h}{H} (b_2 - b_1)$$ where $b_1$ is the length of the shorter base, $b_2$ is the length of the longer base. 3. **Identify given values:** - Shorter base $b_1 = 2$ - Longer base $b_2 = 5$ - Height $H = 1$ - The dotted line is drawn at height $h = 2$ (from the problem statement, the left vertical side is 2, so the dotted line is at height 2 from the shorter base) 4. **Check the height:** Since the trapezoid height is 1, but the dotted line is at height 2, this suggests the dotted line is not inside the trapezoid or the height is misunderstood. The problem states the height is 1, so the dotted line must be somewhere between 0 and 1. 5. **Re-examine the problem:** The left vertical side is labeled 2, which is the height of the trapezoid, so $H=2$. 6. **Calculate the length of the dotted line at height $h=1$ (halfway up):** $$L = 2 + \frac{1}{2} (5 - 2) = 2 + \frac{1}{2} \times 3 = 2 + 1.5 = 3.5$$ 7. **Round to the nearest tenth:** The length is $3.5$. **Final answer:** The length of the dotted line is $3.5$ units.