How to find the length from corner to corner of a rectangle

To find the length from one corner to the opposite corner of a rectangle, you can use the **Pythagorean theorem**. This diagonal length forms the hypotenuse of a right triangle, where the two sides of the rectangle are the legs of the triangle.

Here's the process:

1. Let the length of the rectangle be **L** and the width be **W**.
2. The formula for the diagonal (which is the length from corner to corner) is:

\[
d = \sqrt{L^2 + W^2}
\]

Where:
- **d** is the diagonal length,
- **L** is the length of the rectangle,
- **W** is the width of the rectangle.

### Example:
If the length **L** of the rectangle is 6 units and the width **W** is 8 units, the diagonal is:

\[
d = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ units}.
\]

So, the diagonal is 10 units long.

Would you like more details, or do you have any questions?

### Related Questions:
1. How does the Pythagorean theorem apply to other geometric shapes?
2. What if the rectangle is a square? Does the formula change?
3. How can the diagonal formula help in calculating the area of a rectangle?
4. How does the diagonal change if the length and width of the rectangle increase proportionally?
5. Can we use this formula to find diagonals in 3D shapes like cuboids?

**Tip:** The diagonal is always longer than any side of the rectangle.

Learn how to find the diagonal length of a rectangle using the Pythagorean theorem. The diagonal, forming the hypotenuse of a right triangle, is calculated with the formula d = √(L^2 + W^2). This guide is suitable for students in Grades 6-8.

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