The question from the image asks to find the dimensions of a piece of land that is 800 square meters. The length of the land is given as twice its width.

Let's denote the width of the land as $w$ meters. Therefore, the length of the land would be $2w$ meters.

The area of the rectangle can be calculated using the formula: $\text{Area} = \text{length} \times \text{width}$

Substituting the given values and expression for length: $800 = 2w \times w$ $800 = 2w^2$

We solve for $w$ by dividing both sides by 2 and taking the square root: $w^2 = 400$ $w = 20 \text{ meters}$

Thus, the dimensions of the land are:

• Width = 20 meters
• Length = 40 meters (since the length is twice the width)

Do you have any further questions on this topic, or is there another problem you'd like to explore? Here are a few follow-up questions you might consider:

1. How would the dimensions change if the area of the land were different?
2. What would the dimensions be if the length were three times the width?
3. How would you calculate the perimeter of this piece of land?
4. What is the relationship between the width and length if the ratio were different?
5. How does changing the dimensions affect the area of a rectangle?

Tip: When solving problems involving areas of rectangles, always start by expressing one dimension in terms of the other if a relationship is given. This often simplifies the problem into a single variable equation.