Posted by **alex** on Friday, February 22, 2013 at 3:34pm.

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

- Math question? -
**alex**, Friday, February 22, 2013 at 3:35pm
how to get diagonal saying lenght hight width

- Math question? -
**Reiny**, Friday, February 22, 2013 at 4:23pm
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

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