The image you've provided shows a rectangle with the following dimensions:

• Length: $10x^2$
• Width: $7xy^2$

The perimeter of a rectangle is calculated using the formula:

$\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$

Substituting the given dimensions:

$\text{Perimeter} = 2 \times \left(10x^2 + 7xy^2\right)$

Simplifying:

$\text{Perimeter} = 2 \times 10x^2 + 2 \times 7xy^2$

$\text{Perimeter} = 20x^2 + 14xy^2$

So, the perimeter of the rectangle is:

$\boxed{20x^2 + 14xy^2}$

Would you like further clarification or have additional questions?

Here are 5 related questions for deeper exploration:

1. How do you calculate the area of a rectangle given these dimensions?
2. What if the dimensions were different powers of $x$ and $y$?
3. How would the perimeter change if the width and length were doubled?
4. What is the relationship between the perimeter and the area of a rectangle?
5. How can you apply the perimeter formula to polygons with more sides?

Tip: For any geometric figure, understanding the basic formulas (like perimeter and area) is key to solving many problems quickly!