https://file.aiquickdraw.com/mathbot/file/1738642640431pszioyz8.jpg

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!

Find the perimeter of a rectangle with length 10x² and width 7xy².

Learn how to find the perimeter of a rectangle with algebraic expressions. This problem involves polynomial addition and multiplication, using the perimeter formula 2 × (Length + Width). Suitable for students in Grades 7-10.

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