Question

what is the formula for calculating the length of the space diagonal of a right rectangular prism on the basis of the prism's length l, width w, and height h?

Answer 1

The diagonal of a right rectangular prism is the line that connect opposite vertices. In other word is the distance from corner to corner in the right rectangular prism. Since the diagonal of a right rectangular prism is the hypotenuse of a right triangle, we are going to use a variation of the Pythagorean theorem to find it. In essence, we just need to add another dimension to the Pythagorean theorem; in this case the height of our prism: 

We can conclude that the formula to calculate the length of the diagonal of a right rectangular prism is: $d= \sqrt{l^2+w^2+h^2}$
where
$d$ is the length of the diagonal. 
$l$ is the length of the rectangular base of the prism.
$w$ is the width of the rectangular base of the prism.
$h$ is the height of the prism.