Chapter 8.2, Problem 36WE

To determine

To find: The sketch of the rectangular box and length of a diagonal of the box.

Answer to Problem 36WE

  $\sqrt{l^2+w^2+h^2}$

Explanation of Solution

Given information:

The dimensions of the rectangular box are l, w, h.

Calculation:

The sketch of the rectangular box is drawn below,

The diagonal d of the rectangular box is drawn as below,

The base of the rectangle is drawn below,

Using Pythagoras theorem,

  $a^2=l^2+w^2$

Considering the $\Delta UTR$ ,

Again using Pythagoras theorem,

  $\begin{array}{l}{d}^2=h^2+a^2\\ \Rightarrow d^2=h^2+l^2+w^2[\because a^2=l^2+w^2]\\ \Rightarrow d=\sqrt{l^2+w^2+h^2}\end{array}$

Thus, the length of the diagonal of the rectangle is $\sqrt{l^2+w^2+h^2}$ .