Chapter 8.2, Problem 35WE

To determine

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

Answer to Problem 35WE

  $e\sqrt{3}$

Explanation of Solution

Given information:

The dimensions of the rectangular box are e, e, e.

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,

  $\begin{array}{l}{a}^2=e^2+e^2\\ \Rightarrow a^2=2e^2\end{array}$

Using Pythagoras theorem,

Considering the $\Delta UTR$ ,

Again using Pythagoras theorem,

  $\begin{array}{l}{d}^2=e^2+a^2\\ \Rightarrow d^2=e^2+2e^2[\because a^2=2e^2]\\ \Rightarrow d^2=3e^2\\ \Rightarrow d=\sqrt{3e^2}\\ \Rightarrow d=e\sqrt{3}\end{array}$

Thus, the length of the diagonal of the rectangle is $e\sqrt{3}$ .