the length of a rectangle is twice its width. if the diagonal of the rectangle measures 10 meters, find the dimensions of the rectangle.

To find the dimensions of the rectangle, we can use the Pythagorean Theorem. 

Let's denote:
- The width of the rectangle as \( w \)
- The length of the rectangle as \( l = 2w \)
- The diagonal of the rectangle as \( d = 10 \) meters.

According to the Pythagorean Theorem:

\[
d^2 = l^2 + w^2
\]

Substituting the known values:

\[
10^2 = (2w)^2 + w^2
\]

This simplifies to:

\[
100 = 4w^2 + w^2
\]

\[
100 = 5w^2
\]

Now, solve for \( w \):

\[
w^2 = \frac{100}{5} = 20
\]

\[
w = \sqrt{20} \approx 4.47 \text{ meters}
\]

Now, find the length \( l \):

\[
l = 2w = 2 \times 4.47 \approx 8.94 \text{ meters}
\]

So, the dimensions of the rectangle are approximately:
- Width: 4.47 meters
- Length: 8.94 meters

Would you like further details or have any other questions?

Here are 8 related questions you might consider:

1. What would the dimensions be if the diagonal was 15 meters instead?
2. How would the dimensions change if the length was three times the width?
3. How do you calculate the area of this rectangle?
4. What is the perimeter of this rectangle?
5. If the width was increased by 2 meters, what would be the new dimensions?
6. How would the diagonal change if the width was doubled?
7. What is the relationship between the diagonal and the perimeter of the rectangle?
8. Can the same method be applied to find the dimensions of a square?

**Tip:** Remember that the Pythagorean Theorem is a powerful tool for solving problems involving right triangles, which includes finding dimensions of rectangles when the diagonal is known.

Learn how to find the dimensions of a rectangle when given its diagonal of 10 meters. Use the Pythagorean Theorem to solve for width and length. Detailed step-by-step solution provided. Suitable for Grades 7-9.

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