Chapter 11.6, Problem 11P

To determine

Tofind:the length of each diagonal of the rectangular box. And check whether a meter stick is fit in the box.

Answer to Problem 11P

Yes, $D=101.13cm$ .

Explanation of Solution

Given:

The dimension of the rectangular box is $55\text{cm by }48\text{cm by }70\text{cm}$ .

Calculation:

According to the question, the dimension of the rectangular box is $55\text{cm by }48\text{cm by }70\text{cm}$ .

  

A rectangular box is a three-dimensional solid figure. The square of the main diagonal of any solid can be found by adding the square of the sides.

Therefore, $D^2=l^2+w^2+h^2$

Therefore, the length of each diagonal of the rectangular box is

  $\begin{array}{l}{D}^2=l^2+w^2+h^2\text{ {}\because l=55,w=48,h=70\text{}}\\ D^2={\left(55cm\right)}^2+{\left(48cm\right)}^2+{\left(70cm\right)}^2\\ D^2=\left(3025+2304+4900\right)c{m}^2\\ D^2=10229c{m}^2\end{array}$ .

Taking square both sides, therefore,

  $\begin{array}{l}D=\sqrt{10229c{m}^2}\\ D=101.13cm\end{array}$

As the length of a meter stick is $1m=100cm$ .

So, a meter stick is fit in the box. Since, the diagonal of the box is greater than the length meter stick.

Hence, the length of each diagonal of the rectangular box is $D=101.13cm$ .