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Free online tool that helps you calculate the length of the diagonal of a rectangle based on its width and height.

Diagonal (d)

To calculate the length of the diagonal of a rectangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (in this case, the diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

In the case of a rectangle, the diagonal forms a right triangle with the width and height of the rectangle as the other two sides. Therefore, you can use the Pythagorean theorem to calculate the length of the diagonal as follows:

d² = w² + h²

To get the actual length of the diagonal, you need to take the square root of both sides of the equation:

d = √(w² + h²)

This formula will give you the length of the diagonal of the rectangle, in the same unit of measurement as the width and height of the rectangle. You can use a calculator or an online diagonal of a rectangle calculator to simplify the calculations.

A golden rectangle is a rectangle whose length-to-width ratio is equal to the golden ratio, approximately 1.618. The golden ratio is a mathematical concept that has been studied since ancient times and is believed to have aesthetic and harmonic properties. It is denoted by the Greek letter phi (φ).

In a golden rectangle, the longer side is approximately 1.618 times the length of the shorter side. This ratio is believed to be aesthetically pleasing and is often found in art and architecture, as it is thought to create a sense of balance and harmony.

Golden rectangles also have unique geometric properties. If you cut a square off a golden rectangle, the remaining rectangle is also a golden rectangle. This property is known as self-similarity, and it occurs because the ratio of the lengths of the sides of the original rectangle is the same as the ratio of the lengths of the sides of the remaining rectangle.