How to Find the Length of a Diagonal of a Rectangle

To find the length of a diagonal of a rectangle, you can use the Pythagorean theorem. The diagonal forms a right triangle with the length and width of the rectangle. If you denote the length of the rectangle as a and the width as b, the formula for the diagonal d is:

d = √(a² + b²)

Here’s a step-by-step explanation of how to apply this:

1. Identify the Length and Width: Measure the length and width of the rectangle.
2. Square the Measurements: Calculate the square of the length (a²) and the square of the width (b²).
3. Add the Squares: Add these two values together to get a² + b².
4. Take the Square Root: Finally, take the square root of the result to find the length of the diagonal:

d = √(a² + b²)

For example, if the length of the rectangle is 6 units and the width is 8 units, the diagonal would be:

d = √(6² + 8²) = √(36 + 64) = √100 = 10 units

So, the length of the diagonal is 10 units. This method is not only simple but also effective for any rectangle.