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? [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

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.

$\therefore$ Number of students in a row = a

$\Rightarrow$ Number of students in 'a' rows $=a\times a=a^2$

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

$\therefore a^2=5929$

$\begin{array}{cc}7& 5929\\ 7& 847\\ 11& 121\\ & 11\end{array}$

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

$\Rightarrow a=7\times 11$

$\Rightarrow a=77$

Hence, there are 77 rows in the auditorium.