Question

Calculate the length of the diagonal for the given rectangular prism. It says length hight width

but in the lesson it says length hight deph how to i find the diagonal example

Answer 1

how to get diagonal saying lenght hight width

Answer 2

another simple name for "rectangular prism" is a box
let the
length be x
width be y
height be z

By the diagonal of the box they want the line from a bottom corner to the opposite corner at the top
(think of placing a stick inside the box, where would the longest stick go ?? )

let the diagonal of the base be d
d^2 = x^2 + y^2

now look at the right - angled triangle formed by that diagonal, the height and our stick
let the length of the long diagonal (our stick) be k
then k^2 = d^2 + z^2 , but d^2 = x^2 + y^2
so k^2 = x^2 + y^2 + z^2

e.g. suppose you have a box which is
12 cm by 10 cm by 8 cm
the diagonal = √(12^2+10^2+8^2) = √308 or appr 17.55 cm