Let the width of the rectangle be denoted as $w$.

Since the length is twice the width, the length can be written as $2w$.

The area of the rectangle is given by:

$\text{Area} = \text{Length} \times \text{Width} = 16$

Substitute the expressions for length and width:

$2w \times w = 16$

This simplifies to:

$2w^2 = 16$

Now, divide both sides by 2:

$w^2 = 8$

Take the square root of both sides:

$w = \sqrt{8} = 2.828$

So, the width $w$ is approximately 2.828 meters.

To find the length, recall that the length is twice the width:

$\text{Length} = 2w = 2 \times 2.828 = 5.656 \, \text{meters}$

Final answer:

• Width = 2.828 meters
• Length = 5.656 meters

Would you like further explanation or clarification on any step?

Here are 5 related questions for deeper exploration:

1. How do you derive the formula for the area of a rectangle?
2. Can this method be applied to rectangles with other relationships between length and width?
3. How can we solve for the width if the length is given as a multiple of the width?
4. What happens to the length and width if the area changes to a different value?
5. Can this problem be extended to 3D shapes, like cuboids?

Tip: When dealing with geometric problems involving area and shape relationships, always write down the known relationships first and then translate them into equations.