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.