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= √(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.