Chapter 0.7, Problem 17E

To determine

To evaluate: the longest rectangular panel that can be taken through this doorway.

Answer to Problem 17E

The longest rectangular panel that can be taken through this doorway is 2.66m.

Explanation of Solution

Given information:

It is given that the walls of a recreation center are being covered with paneling.

It is given that the doorway into one room is 0.9m wide and 2.5m high.

The diagram is shown below for given question,

  

In this, AB is height of doorway and BC is the width of room,

AC is the length of the rectangular panel that can be taken through this doorway.

Applying Pythagoras theorem to find the distance from her feet to the top of the pole,

So,

  $\begin{array}{c}{\left(a\right)}^2+{\left(\text{b}\right)}^2={\left(\text{c}\right)}^2\\ {\left(2.5m\right)}^2+{\left(0.9m\right)}^2=c^2\\ 6.25+0.81=c^2\\ 7.06m^2=c^2\\ c=2.66m\end{array}$

So,

The longest rectangular panel that can be taken through this doorway is 2.66m.