Chapter 8.2, Problem 33WE

To determine

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

Answer to Problem 33WE

13

Explanation of Solution

Given information:

The dimensions of the rectangular box are 12, 4, 3.

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,

  $\begin{array}{l}{a}^2={12}^2+4^2\\ \Rightarrow a^2=144+16\\ \Rightarrow a^2=160\end{array}$

Considering the $\Delta UTR$ ,

Again using Pythagoras theorem,

  $\begin{array}{l}{d}^2=3^2+a^2\\ \Rightarrow d^2=9+160[\because a^2=160]\\ \Rightarrow d^2=169\\ \Rightarrow d=\sqrt{169}\\ \Rightarrow d=13\end{array}$

Thus, the length of the diagonal of the rectangle is 13.