Chapter 8.2, Problem 34WE

To determine

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

Answer to Problem 34WE

  $3\sqrt{6}$

Explanation of Solution

Given information:

The dimensions of the rectangular box are 5, 5, 2.

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,

  $\begin{array}{l}{a}^2=5^2+5^2\\ \Rightarrow a^2=25+25\\ \Rightarrow a^2=50\end{array}$

Considering the $\Delta UTR$ ,

Again using Pythagoras theorem,

  $\begin{array}{l}{d}^2=2^2+a^2\\ \Rightarrow d^2=4+50[\because a^2=50]\\ \Rightarrow d^2=54\\ \Rightarrow d=\sqrt{54}\\ \Rightarrow d=3\sqrt{6}\end{array}$

Thus, the length of the diagonal of the rectangle is $3\sqrt{6}$ .