To solve for $x$, the length of $QR$, we use the fact that the quadrilaterals $JKLM$ and $PQRS$ are similar. Similar polygons have corresponding sides proportional.

Step-by-Step Solution:

1. Identify corresponding sides:

   • From the figure:
     • $JK$ (length $4$) corresponds to $PQ$ (length $2.4$).
     • $JM$ (length $5$) corresponds to $PS$ (length $3$).
     • $LM$ (length $6$) corresponds to $RS$ (length $3.6$).
     • $KL$ (length $3$) corresponds to $QR$ (length $x$).

2. Set up a proportion: The ratio of corresponding sides is the same for all sides in similar quadrilaterals. Using the sides $JM$ and $PS$ to calculate the ratio: $\text{Ratio} = \frac{\text{PS}}{\text{JM}} = \frac{3}{5}.$ This ratio applies to all corresponding sides.

3. Solve for $x$: Use the side $KL$ and $QR$: $\frac{\text{QR}}{\text{KL}} = \frac{3}{5}.$ Substitute the known values: $\frac{x}{3} = \frac{3}{5}.$ Solve for $x$ by cross-multiplying: $5x = 3 \cdot 3 \quad \implies \quad 5x = 9.$ Divide both sides by 5: $x = \frac{9}{5} = 1.8.$

Final Answer:

The length of $QR$ is 1.8 units.

Let me know if you would like further clarifications! Here are 5 related questions for practice:

1. How do you determine if two polygons are similar?
2. What are the properties of similar triangles and quadrilaterals?
3. How do you solve for unknown side lengths in proportional relationships?
4. How can you check if two given ratios are equal?
5. If two sides in a quadrilateral are doubled, how does the ratio change?

Tip: Always identify corresponding sides clearly when working with similar polygons.