Question

5929 students are sitting in an auditorium in such a manner that there are as many students in a row as there are rows in the auditorium. How many rows are there in the auditorium?​

Answer 1

Answer:

Step-by-step explanation:

Let there be  

′

a  

′

 rows in the auditorium

Since the number of students in a row is same as the number of rows in the auditorium.

∴ Number of students in a row =a

⇒ Number of students in  

′

a  

′

 rows =a×a=a  

2

 

It is given that the total number of students in the auditorium =5929.

∴a  

2

=5929

⇒a=  

5929

​

 

7∣5929

7∣847

​

 

11∣121

​

 

∣11

​

 

⇒a=  

(7×7)×(11×11)

​

 

[By prime factorisation]

⇒a=7×11 [Taking one factor in each pair]

⇒a=77

Hence, there are 77 rows in the auditorium

Answer 2

Let there be ′a′ rows in the auditorium

Since the number of students in a row is same as the number of rows in the auditorium.

∴ Number of students in a row =a

$\small \bold{⇒ Number \: of \: students \: in \:  a \: rows =a×a= {a}^{2}}$It is given that the total number of students in the auditorium =5929.

$\therefore \: {a}^{2} = 5929$

$\rightarrow \: a = \sqrt{5929}$

7∣5929

7∣847

11∣121

∣11

$\implies \: a = \sqrt{(7 \times 7) \times (11 \times 11)}$

[By prime factorisation]

⇒a=7×11 [Taking one factor in each pair]

⇒a=77

Hence, there are 77 rows in the auditorium.