Chapter 14.3, Problem 32E

To determine

To calculate: The length of each part.

Answer to Problem 32E

Option C is correct.

Explanation of Solution

Given information:

A carpenter divides a board that is 7 feet 9 inches long into three equal parts..

Formula used:

Circular Permutations :- If n objects are arranged in a circle, then there are $\frac{n!}{n}\text{ or }\left(n-1\right)!$ permutations of the n objects around the circle.

Calculation:

According to the question,

Length of the board is 7 feet 9 inches.

Total parts are 3.

  $\begin{array}{l}=1\text{ feet}=12\text{ inches}\\ =7\text{ feet}=12\times 7\text{ inches}\\ =84\text{ inches}\end{array}$

Therefore, the length of the cardboard is

$\begin{array}{l}=(84+9)\text{ inches}\\ =93\text{ inches}\end{array}$

Now, length of each part is

$\begin{array}{l}=\frac{\text{Total length of the cardboard}}{\text{Total equal parts}}\\ =\frac{93}{3}\\ =31\end{array}$

The length of each part is $31\text{ inches}$ .

  $\begin{array}{l}=1\text{ inches}=\frac{1}{12}\text{ feet}\\ =31\text{ inches}=\frac{31}{12}\text{ feet}\\ =2\text{ feet }7\text{ inches}\end{array}$

Hence , the length of each part is $$

  $2\text{ feet }7\text{ inches}\text{.}$