MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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: [tex]d= \sqrt{l^2+w^2+h^2} [/tex]

where

[tex]d[/tex] is the length of the diagonal.

[tex]l[/tex] is the length of the rectangular base of the prism.

[tex]w[/tex] is the width of the rectangular base of the prism.

[tex]h[/tex] is the height of the prism.

We can conclude that the formula to calculate the length of the diagonal of a right rectangular prism is: [tex]d= \sqrt{l^2+w^2+h^2} [/tex]

where

[tex]d[/tex] is the length of the diagonal.

[tex]l[/tex] is the length of the rectangular base of the prism.

[tex]w[/tex] is the width of the rectangular base of the prism.

[tex]h[/tex] is the height of the prism.