The formula for calculating the length of the diagonal (d) of a right rectangular prism can be expressed as:
d = √(l² + w² + h²)
Where:
- l = length of the prism
- w = width of the prism
- h = height of the prism
To break this down further, a right rectangular prism has three dimensions: length, width, and height. The diagonal runs from one corner of the prism to the opposite corner, crossing through the interior space of the prism. By applying the Pythagorean theorem in three dimensions, we can sum the squares of these three dimensions and then take the square root to find the length of the diagonal. This formula is useful in various fields such as architecture, engineering, and design, as it helps in determining the maximum length of a line that can fit inside the prism.