https://r2.erweima.ai/mathbot/image/1725915356256jkkh16k4.jpg

Let's break down the problem step by step:

1. **Given Conditions:**
   - The length (L) of the rectangle is twice its width (W), so:  
     \[
     L = 2W
     \]
   - The area (A) of the rectangle is 50 cm², and the formula for the area of a rectangle is:  
     \[
     A = L \times W
     \]

2. **Set up the equation using the area:**
   Since \( L = 2W \), substitute this into the area formula:
   \[
   A = 2W \times W = 2W^2
   \]
   Given that the area is 50 cm²:
   \[
   2W^2 = 50
   \]

3. **Solve for the width (W):**
   \[
   W^2 = \frac{50}{2} = 25
   \]
   \[
   W = \sqrt{25} = 5 \, \text{cm}
   \]

4. **Find the length (L):**
   \[
   L = 2W = 2 \times 5 = 10 \, \text{cm}
   \]

5. **Calculate the perimeter (P):**
   The formula for the perimeter of a rectangle is:
   \[
   P = 2L + 2W
   \]
   Substituting the values of \( L \) and \( W \):
   \[
   P = 2(10) + 2(5) = 20 + 10 = 30 \, \text{cm}
   \]

Thus, the perimeter of the rectangle is **30 cm**.

Would you like more details, or have any questions on this?

Here are 5 related questions for practice:
1. If the width of the rectangle was increased by 2 cm, what would its new perimeter be?
2. If the length of the rectangle was three times its width, how would that affect the perimeter?
3. What is the diagonal of the rectangle based on the given dimensions?
4. If the area of a different rectangle is 72 cm², and the length is twice its width, what would its perimeter be?
5. How would you find the perimeter if only the area and diagonal were given?

**Tip:** For any rectangle, if you know the area and the ratio of the sides, you can always use algebra to find both the width and length.

The length of a rectangle is twice its width. If the area of the rectangle is 50 cm², find its perimeter.

Learn how to find the perimeter of a rectangle when the length is twice its width, and the area is 50 cm². This problem demonstrates the use of geometry and algebra to solve for the dimensions and perimeter. Suitable for Grades 6-8.

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