+0  
 
0
43
1
avatar

A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column. If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing 36 chairs? Note that 12 rows of 3 chairs is different from 3 rows of 12 chairs.

Guest Jun 26, 2018

Best Answer 

 #1
avatar+19603 
+2

A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column. If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing 36 chairs? Note that 12 rows of 3 chairs is different from 3 rows of 12 chairs.

 

The divisors of 36 are: 1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36 (9 divisors)

 

There must be at least two chairs in every row and column:

The result is:

\(\begin{array}{|l|rcl|} \hline & &\text{array}& \\ \hline 1. & 2 &\times& 18 \\ \hline 2. & 18 &\times& 2 \\ \hline 3. & 3 &\times& 12 \\ \hline 4. & 12 &\times& 3 \\ \hline 5. & 4 &\times& 9 \\ \hline 6. & 9 &\times& 4 \\ \hline 7. & 6 &\times& 6 \\ \hline \end{array}\)

 

7 arrays are posible in a classroom containing 36 chairs?

 

laugh

heureka  Jun 26, 2018
 #1
avatar+19603 
+2
Best Answer

A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column. If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing 36 chairs? Note that 12 rows of 3 chairs is different from 3 rows of 12 chairs.

 

The divisors of 36 are: 1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36 (9 divisors)

 

There must be at least two chairs in every row and column:

The result is:

\(\begin{array}{|l|rcl|} \hline & &\text{array}& \\ \hline 1. & 2 &\times& 18 \\ \hline 2. & 18 &\times& 2 \\ \hline 3. & 3 &\times& 12 \\ \hline 4. & 12 &\times& 3 \\ \hline 5. & 4 &\times& 9 \\ \hline 6. & 9 &\times& 4 \\ \hline 7. & 6 &\times& 6 \\ \hline \end{array}\)

 

7 arrays are posible in a classroom containing 36 chairs?

 

laugh

heureka  Jun 26, 2018

11 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.