We are given that quadrilateral LMNO is similar to quadrilateral PQRS. This means their corresponding sides are proportional.

Step 1: Identify the Given Side Lengths

• LM = 3
• OL = 7
• PQ = ? (this is what we need to find)
• SP = 25

Step 2: Set Up a Proportion

Since the quadrilaterals are similar, the ratio of corresponding sides is the same. We use the vertical sides OL and SP to set up the proportion:

$\frac{LM}{PQ} = \frac{OL}{SP}$

Substituting the known values:

$\frac{3}{PQ} = \frac{7}{25}$

Step 3: Solve for $PQ$

Cross-multiply:

$3 \times 25 = PQ \times 7$

$75 = 7PQ$

$PQ = \frac{75}{7} = 10.7$

Final Answer:

$\mathbf{PQ = 10.7}$

Do you have any questions or want a more detailed explanation?

Here are some related questions to think about:

1. How do we know that two quadrilaterals are similar?
2. What is the property of similarity in geometry?
3. Can we use the same proportion to find another missing side?
4. How does scaling affect the perimeter of similar shapes?
5. What happens to the area when a shape is scaled up?

Tip: When working with similar figures, always check that you're comparing corresponding sides correctly!