https://file.aiquickdraw.com/mathbot/file/1726220741349x4y6x7cm.jpg

To find the perimeter of the rectangle, we use the perimeter formula for a rectangle:

\[
P = 2 \times (\text{Length} + \text{Width})
\]

From the image:

- Length \( = 5\sqrt{3} \)
- Width \( = 2\sqrt{11} \)

Now, we substitute the values into the perimeter formula:

\[
P = 2 \times \left( 5\sqrt{3} + 2\sqrt{11} \right)
\]

Since the two terms under the square roots are different, they cannot be combined directly. Therefore, the perimeter in its simplest radical form is:

\[
P = 2 \times (5\sqrt{3} + 2\sqrt{11}) = 10\sqrt{3} + 4\sqrt{11}
\]

Thus, the perimeter of the rectangle is:

\[
P = 10\sqrt{3} + 4\sqrt{11}
\]

Would you like any more details or explanations?

Here are some related questions you could explore:
1. How do we simplify the expression \( 10\sqrt{3} + 4\sqrt{11} \)?
2. Can the length and width of any other rectangles be expressed in radical form?
3. What would happen if the length and width had the same square roots?
4. How can we calculate the area of this rectangle?
5. What are some real-world applications of using radicals in geometry?

**Tip:** When adding or subtracting radicals, always check whether the values inside the square roots are the same before attempting to simplify further.

Find the perimeter of the following rectangle. Give your answer in simplest radical form. (Length = 5√3, Width = 2√11)

Learn how to find the perimeter of a rectangle where the length and width are expressed in radical form. This problem uses geometric formulas and radical expressions, suitable for students in Grades 9-12.

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