We are tasked with finding the length of $QR$ in the two similar quadrilaterals $JKLM$ and $PQRS$. Since the quadrilaterals are similar, the sides are proportional.

Step 1: Identify corresponding sides

From the given image:

• Side $JL = 6$ corresponds to $QR = x$,
• Side $JM = 5$ corresponds to $PS = 3$,
• Side $KL = 3$ corresponds to $PQ = 2.4$.

Step 2: Set up the proportion

We use the corresponding side lengths to set up a proportion. Let $x$ represent $QR$, and we use the ratio between sides $JM$ and $PS$, which is: $\frac{JM}{PS} = \frac{6}{QR}$ Substitute the known values: $\frac{5}{3} = \frac{6}{x}$

Step 3: Solve for $x$

Cross-multiply: $5x = 6 \cdot 3$ $5x = 18$ Now divide by 5: $x = \frac{18}{5} = 3.6$

Final Answer:

The length of $QR$ is 3.6 units.

Questions for you:

1. Would you like a visual diagram to explain similar polygons and proportions?
2. How do you calculate side lengths for other similar polygons?
3. What happens if two polygons are not similar?
4. Can we verify proportions with real-world measurements?
5. Would you like practice problems on similar triangles and quadrilaterals?

Tip:

When working with similar shapes, always check corresponding sides carefully to set up the correct ratios.